Econo-Physics a Perspective of Matching Two Sciences

ARTICLE

Econo-physics: A Perspective of Matching TwoSciences

Yuri YEGOROV

Institute for Advanced Studies, Stumpergasse 56, A-1060, Vienna, Austria, and University ofVienna, Department of Industry and Energy, Brünner Strasse, 72, A-1210, Vienna, Austria. E-mail: [email protected]

AbstractThe present article marks some potentially fruitful dimensions of economic research basedon principles of economic theory but using more analogies with physics. Molecularstructure of society with its different states, principles generating spontaneous orderdifferent from “invisible hand”, social analogies of the concepts of temperature and pressurein physics are investigated. Some analogies between phase transitions in physics andtransition between different social regimes can reveal the areas of stability of liberal regimesas well as possibility of spontaneous emergence of different social orders. A possibility toexpand neoclassical economics to capture Marxism and nationalism in a formalmathematical framework is also discussed.Keywords: economic structures, origin of order, econo-physics, socio-physics.

1. Introduction

This article is methodological. It focuses on economic and social questions that are

rarely touched by economic theorists despite their obvious importance for our

understanding of economic processes in the world. No fully formalized model will be

proposed here. Instead, the focus will be on interaction between economic elements and

emergence of structures. These ideas have been successfully elaborated in natural

science by physicists. That is why it makes sense to look for some analogies between

physical and economic concepts, and then to find ways of employing principles of

modelling from physcis into economic science.

The term “econophysics” is already used in narrow sense, to describe models of

financial markets using some ideas from physics (see Mantegna and Stanley, 2000).

However, the cross-fertilization between these two sciences allows for a wider treatment.

That is why here we will use another word “econo-physics” (and sometimes “socio-

physics”), following the paper by Aruka and Mimkes (2006) in order to escape

Evol. Inst. Econ. Rev. 4(1): 143–170 (2007)

JEL: B41, B51, B52, F02, P25.

misunderstanding in terminology. While the word “socio-physics” was not commonly

accepted among scientists that work in this field, there exist fundamental contribution to

this field from such authors as Haken (1977) and Weidlich (2002).

1.1 Motivation

The main goal of this paper is to describe directions of fruitful explorations, based on

past positive experience of physics and taking into account specific economic

assumptions. There is no criticism here about microeconomic preferences, but more

about little explored directions in economic science. The other goals of this article are:

a) to put some of the ideas into a language more common for economists (thus, not to

escape utility function, etc);

b) to describe different social organizations and ideologies of society (nationalism,

Marxism) in a mathematical framework that naturally extends classical economics;

c) to discuss multiplicity of social order-generating principles;

d) to discuss phases and phase transition in society.

Physics is a science about structures, their emergence and transformation. All the

nature has different level of organizations, and macro properties can be derived on the

basis of micro elements and interactions between them. Economics seems to move a

similar path, since agents are considered as fundamental elements, like atoms in physics.

However, economics at present is linear science in a sense that it puts an individual at the

absolute level and does not consider endogeneous emergence of structures of

individuals. Clearly, the primitives may be not individual agents but firms (in industrial

organization) or countries (in macroeconomics). However, little is done to understand

what kind of interactions bring individuals to the further level of organization (firms,

countries, etc). Physics has great experience of building links between micro and macro

levels. Statistical physics is the branch of physics that derives the changes of macro

states of matter through micro parameters. The theory of waves in continuous media

focuses on the link between micro and macro levels but in different research field. There

the local interaction between small subsets (neighbourhoods) leads to emergence of

complex dynamics in space and time. Physical chemistry studies the transformation of

properties of matter when coupling occurs at the level of (elementary) atoms that can

form different types of molecules. Finally, nuclear physics is about transformations

inside atoms changing their structure.

Clearly, not all of these transitions from micro to different macro levels can be

successfully implemented in economics. For example, changing internal structure of

atom would mean, if we employ the analogy between atom and economic agent, the

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change of agent’s nature. It may be of biological or psychological origin, but typically

economics consider individuals as stable over time. This change, for example evolution

of preferences with ageing, can be an interesting economic question, but it will not be

elaborated here. There also exist some problems with application of mathematically rich

theory of waves to economics. The problem is that there are too few observations

confirming existence of economic processes with deterministic cyclical origin. But while

economics is unlikely to give very rich field for mathematical models of regular wave

structures with deterministic nature, there still exist some works in this direction. That is

why analogies with statistical mechanics and physical chemistry might find easier

application in economic models. And this paper will concentrate more on these issues.

Section 2 is oriented on the necessity of common language of economics and physics

in order to deal with the phenomena of molecular structure of society. Section 3 is

devoted to origins of social order, that are complementary to market forces. Section 4

introduces thermodynamic concepts for society (analogies of temperature and pressure)

and describes several social types (solid, liquid and gas) that depend on combination of

these parameters. The role of altruism in preferences is discussed in Section 5. This goes

in line with new concepts elaborated in the book of Bowles (2003). Moreover, adding

altruism into preferences allows to describe not only liberal society (like neoclassical

economics does) but also societies of Marxist and nationalist types. Altruistic

preferences bring more solid grounding to emergence of social structures. Existing types

of equilibria developed by non-cooperative game theory are rather weak and unstable,

while even small altruistic element can make them more robust. An example is provided.

Section 6 deals with potential applications.

1.2 Link with modern paradigms in sciences

The agenda presented in abstract is unusual for a paper in economic theory. An important

aspect is related to heterogeneity and structure. While it is true that physicists also

consider the world to be formed of a large number of elementary objects (atoms from the

time from Aristotle to Newton, and elementary particles or quarks at later stage), these

particles are interacting not equally with each other, since this interaction depends on

distance and since they are located in different points in space at any time moment.

Clusters of particles form different structures starting from molecules and ending with

crystals. This gives self-evolving patterns, which at one level of abstraction can be

described as wave motion and at the other level as phase transition.

My agenda would be not in putting in doubt some mutually recognized principles of

economic science but rather to focus the attention on its limitation in conceptual sense.

Econo-physics: A Perspective of Matching Two Sciences

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That is why I want to keep all these assumptions about utility and rationality, but to

consider also some other conditions (acting as external forces). Different sections would

deal with some philosophical and methodological aspects of creating models in

economics.

1.3 Related literature

The ideas of unified science, including economics and physics, have been expressed

more than a century ago. The 120-year old ideas of Serhij Podolinsky to combine

Marxism with ecology have been rejected by Marxists. Proposal for unified science was

expressed by Otto Neurath in 1920s.1) Economics should include physical aspects of

human ecology, study of cultural, social, ethical influences on production and

consumption (see Krishan et al. (1995)).

This agenda became critically important in the last 3 decades of the 20th century,

when ecologists realized the danger of combining the reality of exhaustible resources

with the continuing growth of population and production. The necessity of ecological

economics was formulated by Goodwin. He proves the existence of substantial set of

questions, which are addressed to real economic problems and located on the frontier of

traditional economic science, and tries to study questions on the intersection of different

sciences. He says that “if the study of economics is to be of value to society it must stress

the aspects of economic behaviour that matter the most”.2) A number of critical areas of

economic thought have been left by mainstream economists on the margin. He argues

that while the relevant agenda was formulated by classics of economics in the past, some

priorities have been shifted later. For example, Adam Smith put similar value to the

concepts of wealth, morality and nation, but currently the last two concepts are out of

interest of mainstream economics. Similarly, von Thünen in 1826 pioneered the research

of spatial economic structures, which later became a part of regional science, but this

field is left out of major economic textbooks in microeconomics.

Ecological economics, although inspired by ecological degradation and ideas of

sustainable development, is not a science of ecology, but also addresses the questions of

evolution of purely economic systems (see ch. 8 in Faber et al. (1996)). The authors use

a parallel between physics, theoretical biology and economics and try to classify what

processes are predictable and non-predictable in all these sciences. Physical systems

exhibit the highest degree of predictability, due to lower complexity, partly in

deterministic and partly in stochastic terms. This was the major reason of successful

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1) See the summary of “The history of future” by J. Martinez-Alier and K. Schluppman there.2) See introduction to the book by Krishan et al. (1995)

development of mathematical tools describing dynamical systems in physics. Economics

also exhibit phenomena, which are completely predictable, and establishing of market

equilibria is one of such phenomena. However, economics does not use all available

techniques from physics to explain other classes of processes that are also predictable.

The difficulty of economic modelling can be easier understood on the basis of statement

of theoretical biology about “fundamental unpredictability of genotypic evolution”, in

contrast to phenotypic evolution. The economic analogy of genotype is innovation.

While evolutionary path after innovation occurs can be predicted, the moment of

innovation cannot.

Here the issues of non-predictability and evolution will not be substantially

elaborated. Instead, more attention will be paid to structures and mechanisms of their

emergence and survival under changing conditions. This already represents wide

direction of research, and little analytical work was done here by economists so far.

A nice exception is the book of Bowles (2003), where he suggests evolutionary theory

of institutions. Non-market social interactions represent one of key points of his

research. He studies co-evolution of individual preferences and structures of markets

using dynamic models. This agenda differs substantially from one delivered by classical

microeconomics, but it allows to explain much more historical episodes and empirical

puzzles.

In the article by Aruka and Mimkes (2006) different areas of influence of physical

ideas on social sciences and economics are discussed. The importance of considering

heterogeneous interacting agents is stressed. While agents’ heterogeneity is sometimes

present in economic models,3) most of classical economic papers deal with homogeneous

individualistic agents. Such an approach is easier from methodological perspectives,

because it allows to build self-consistent economic theory based on rationality principles,

while heterogeneous assumption often requires the shift to bounded rationality.

Following the principles of homogeneity and full rationality limits the possibility of

modelling real social phenomena (like wealth distribution) and broadens the gap between

theoretical and empirical economics.

The role of synergetics (see Haken (1977)) in understanding social dynamics is

important. There are two levels: micro and macro. Macrodynamic evolution is

dominated by few key variables, named order-parameters. Macro states of a social

system are described in probabilistic terms. The central equation of evolution for the

probability distribution over the macro variables is called Master equation (see Weidlich


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3) In fact, WEHIA conferences by definition deal with this type of agents.

(2002, 2006)).

The main claim of the work by Bowles and Gintis (2005) is that “other-regarding

preferences such as altruism and reciprocity are essential” for understanding why

humans are cooperative. At the first glance, cooperation often takes place even if the

preferences are self-regarding (like in almost all research of economics). However, these

theories are not sufficient to explain all evidence. For example, reciprocal altruism

provide some explanation of cooperation among dyads, but not in larger groups and

when future interactions are unlikely.

Kara-Murza (2002) writes that Thomas Gobbs has developed the myth about man as

egoistic and individualistic atom. These “atomic” ideas emerge every time when ruling

groups want to impose liberal economics in the society. Emergence of industry and

market economy required the freedom of a man from conservative political, economical

and cultural structures. The ideas of atomism and rationality allow solving two

ideological tasks of rising bourgeoisie: to legitimate new political order and new

economic order.

Skirbekk (2003) analyses the negative influence of the presently dominant liberal

ideology on social moral, growing instability of family and argue about the missed

positive elements of traditional cultures and ideologies that went to decline in the end of

the 20th century.

Emergence of structures (large groups, countries) resembles emergence of molecules

or crystals from atoms. In physics, this requires the field of interaction. The standard

assumptions of economic theory (self-regarding preferences, non-convexities) do not

allow for emergence of such structures. Thus they are either considered as given (firm,

state) or not considered at all. The papers of Yegorov (2001b, 2005a) study the

emergence of such groups on the assumption of non-convex technology that makes it

optimal for group members to keep group growing in a dynamic sense until it reaches its

optimal size. Also, the conditions of country emergence are considered. It is shown that a

territory of certain size becomes an optimal structure for its inhabitants (assumed to be

homogeneous) when we move from micro to macro level and consider the balance

between benefits from harvesting certain territory and the costs to protect its border and

to maintain centralized structure that needs communication with all points (regions) for

efficient management.

As will be claimed later, both spatial structures in economics (location heterogeneity

plus transport cost) and scale economies play important roles as origins of order in

society. Some ideas of the author in both of these areas can be taken from Yegorov

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(1998, 2001ab, 2005ab).

2. Working Out Common Language between Economics and Physics

The tragedy of contemporary science is an increased specialization, leading to

impossibility of general public to understand science. This property was mentioned by

Kuhn (1970). That is why one cannot use the language of most sophisticated concepts

inside physics and economics. In order to be understandable to more scientists, it is

better to use relatively simple concepts from both sciences and to find link across them.

Only simple concepts from physics such as “particles”, “state of matter”, “field”,

“energy”, which are studied in school, will be employed here. Economic concepts of

similar simplicity would be employed as analogy. I am fully aware that complete

analogy is impossible, but even incomplete analogy can be powerful. Below I introduce

several concepts that can be used as approximate translations from language of “physics”

to “economics” and visa versa.

Elements

The elements in physics are “particles”, “atoms”, while in economics the analogy is

played by “agents”. Clearly, there is a difference since particles cannot think, while

agents obey laws of behaviour different from particles. But the analogy can be exploited

when we are doing aggregation and consider nonlinear interactions between elements.

Simple structures

In physics “molecules” represent a relatively stable union of a small number of atoms.

Similar structures also exist in economics; for example, family or small business.

Complex structures

In physics complex structures emerge on macro level. In statistical physics, the micro-

state is a set of many particles with their coordinates and velocities (which is never

completely observed). The parameters of macro-state (temperature, pressure) can be

measured. Physics knows how to interrelate macroparameters with distribution of micro-

parameters. Economics is addressing similar models when it talks about aggregation,

from micro to macro level.4) Economy, state or global society are examples of complex

structures in economics.

Interaction

In physics, particles interact via the field. All fields are usually declining with distance

according to a particular inverse power law. The coordinates of particles make them

naturally asymmetric with respect to field. Depending on initial conditions, different


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4) See the papers of Hildenbrandt.

structures can emerge. For example, gravity force has created a system of planets. On

micro-level, molecules are stable structures of the field generated by particles. It is

worthwhile mentioning that nonlinearity and heterogeneity are responsible for

emergence of most structures. In economics, interaction is usually modelled as linear:

agents contribute their endowments to the market, and take other products from there,

according to their preferences. The only nonlinearity can come from utility, but as it is

ordinal, this nonlinearity does not play a crucial role. Nevertheless, markets exhibit self-

organizing property.5) Non-linear element of interaction among agents is given by

externalities. The potential of externalities in building stable structures in economics is

still under-exploited, and one of the goals of present work is to attract attention to this

problem.

Characteristics of elements

In physics, particles are characterized by their coordinates, velocities and energies. Due

to Heisenberg inequality from quantum mechanics, the first two parameters cannot be

measured exactly on micro level. On the other hand, energy can be defined and

measured. Economic science may also have a type of Heisenberg inequality, because

some microeconomic parameters (like utility) are not observable directly. This is an

interesting question, however it is not developed yet. In economics, an analogy of

coordinates and velocities can be given by dynamic pattern of consumption bundle,

while “wealth” (or income) is an analogy of energy. The latter can be easier observed.

Thus, macroeconomic state should depend on wealth distribution of agents, which is

measurable in reality. The role of wealth distribution for the stability of social structures

will be discussed later.

Characteristics of structures

Structures in physics can be characterized by their total energy, mass, entropy, type of

micro-order (crystal or gas, for example). In economics, macroeconomics deals with

country’s GDP, interest rate, growth rate, etc. The parameters characterizing type of

order (see section 3) are usually not studied by economics, although they represent an

important macro characteristic of society.

2.1 Molecular structure of society

Classical microeconomics and industrial organization consider the number of firms as

given. Thus, they view firms like mechanics views atoms, but do not allow for an

analogy of chemical reactions. In real business, firms may split, join together, be born

and die.

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5) In the sense that they generate equilibrium under certain assumptions (see Arrow-Debreu theory).

Molecules of firms can form chains with local interaction. This is similar to a structure

of polymer. The idea of “polymer society” is represented in the studies of network

economics, especially the part related to emergence of random networks with short-scale

or long scale links.6)

Structures can be imposed (by state) or self-organized (emergence of small firms of

Italian type, with about 10 workers, mostly relatives; or agricultural cooperatives). The

influence of state on economy is studied by economics of public sector (see the book of

Stiglitz (1988) as an example). Self-organization of structures can occur on the basis of

mixed utility (see mathematical model subsequently). Physical analogy: forced order or

crystallization in external field vs. spontaneously emerging clusters.

Different particles of physical substance have different energy, and stable distribution

of their velocities in gas can be an analogy to stable distribution of wealth in particular

societies. This question of wealth distribution deserves special attention and will be

briefly elaborated later.

3. Equilibrium, Structure and Order in Economics

The concept of equilibrium plays the major role in theoretical economics. The principle

of equilibrium was brought to economics from mechanics. Equilibrium world was

neither scientific nor logical conclusion. Equilibrium in economics was not a discovered

law. Contrary, the search for economic laws was based on beliefs in equilibrium. All

economics (political economy) starting from Adam Smith, neglects all sources of

disequilibrium (see Kara-Murza (2002), pp. 124–125).

3.1 Why structure is important?

When we look at structures in natural sciences (physics, chemistry, biology), we find that

structure is some composition of elements which is relatively stable under some range of

external parameters and thus can be observed. For example, some chemical elements are

observed on earth in natural conditions, while other need some special laboratory

conditions. Species and populations are biological structures, also composed of elements.

When they die, they are decomposed back to sub-elements. In social sciences, structures

include some composition of elementary agents: firms, clubs, countries, mankind.

Neoclassical economics does not pay much attention to these structures. However, even

its father, Adam Smith stressed the importance of states and nations as objects of study

of economics. Neoclassical economics exploits another idea of Smith, “invisible hand”,


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6) See Stocker et al. (2000); there are also many unpublished drafts presented at conferences and

seminars.

which brings spontaneous order by market forces. Despite the relative success of this

idea for explaining spontaneous order, it is clear that it is incomplete.

3.2 Structures and transition in Russia

Application of ideas from neoclassical economics with welfare theorems to transition in

Russia in 1992 was not a successful experiment. Only in 1999 J. Stiglitz has recognized

that this type of transition was a mistake for Russia. Many structures have been

destroyed during transition of 1990s. It was clear that changing environment should

destroy some of the old order, but it is not clear how new order can emerge from chaos.

Global shocks on Earth have led to death of some populations (dinosaurs). But they are

not replaced immediately by new types of species. When a biological object dies, it

dissolves into molecules, which give rise to emergence of some low-structured life

(bacterias). It takes long time for evolution, for life of higher complexity to emerge. If

the higher level of economy (high-tech industry) is dead during transition in a particular

country (Russia), elements (capital and labour) become free. But capital in a form of

constructions may become obsolete, while labour can find itself facing the only

possibility to start individual activity or small business. It takes some time for high-level

firms to organize on these ruins, and the only possibility is takeover by transnational

companies. However, in 1990s capital was not flowing freely in Russia, and one reason

behind that was described by Parshev (2001). I will not focus now more on transition.

The goal was to show that study of emergence of structures is crucial and should be hot

topic for modern economics which wants to explain processes in real but not imaginary

world of abstract spaces that some part of modern economic theory does.

3.3 Origins of order in society

It is important to formulate this philosophical question about origins of social order.

While it is clear that its substantial investigation in one isolated article is impossible, it

still makes sense to suggest some working hypothesis.

There exists at least three main forces generating spontaneous order in economy. The

first one is well known from microeconomic textbooks. It is linked with market forces

caused by diminishing returns and competition (they are responsible for the effect of

Adam Smith’s “invisible hand”).

The second force comes from studies in regional science and economic geography

(see, for example, Beckmann and Thisse (1986)). This force may bring complementary

properties to those derived by non-spatial economic theory. For example, monopolistic

competition of Chamberlin (1933) reveals the existence of spatial areas around a firm

when they act as local monopolists and compete only through edge consumer.

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Monopolistic competition with product differentiation (see, for example, Fujita,

Krugman and Venables (1999)) rely on completely different case (methodological and

topological), where consumers have access to all variety of commodities. Spatial forces

based on transport cost and local interaction become responsible for geographical,

location effect, which are always present and cannot be fully controlled by rational

decisions. Some spatial effects are elaborated by Yegorov (2005b).

The third self-organizing principle is based on nonlinear interaction of elements (when

the whole is not exactly sum of its parts). Without trying to present sufficient literature

survey on this topic, I will just mention two important publications: Arthur (1994) and

Durlauf and Young (2001). This principle summarizes the self-organizing role of

externalities. They can bring the difference between social outcome and individual

preferences (like in segregation model of T. Schelling). They often lead to multiplicity of

equilibria, also in dynamic sense.

Role of space

Space works as an element imposing heterogeneity (at least, with respect to distance),

and thus bringing nonlinearity to interaction of a priori identical elements.7) But space

also works as a stabilizing factor. For example, the IRS technology in a spaceless context

gives rise to a firm of infinite size. With transport costs and topology of real geographical

space, optimal cooperation extends to a particular spatial limit (see Yegorov (1998,

2001a)).

Analogy with different sciences

This duality between market and spatial forces is similar to one argument of social

scientists about the role of biology and environment in human beings. Most likely,

humans are not fully predetermined by genetics. Maugli’s example shows that an

important part of individual formation depends on the environment. However, it would

be too far-fetched to expect that everything depends on environment and has no relation

to genetics and biology. Economists (except for regional scientists) mostly ignore the

spatial forces. Another extreme view (complete geographic predetermination) is also

unlikely to be true.


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7) Hence, agents equal in skills become unequal just due to location difference. This contrasts an

approach of urban economics where at equilibrium such agents have a possibility to change location

but are indifferent to do it. Frictions and historical factors might make this inequality persistent (like

people got used to less productive land and not all migrate to the region where they would have higher

productivity.)

It makes sense to describe the mechanism of self-organization of spatial structures in

economics. Geographical forces are considered as “gravity” by some economists, with

complete copying of inverse power8) Newton’s law, and this has no microeconomic

justification. But it is possible to build a simple model describing an emergence of a

country of optimal size (Yegorov, 2005a) based on the principles of optimization,

transport costs and Euclidean geometry applied to continuous space.

Order-generating principles

It makes sense to end this discussion with a potentially incomplete list of principles that

generate order.

1. A common idea (religion, nation) can be responsible for non-market grouping of

large number of people. Historically such groups had leaders accepted by all. This

leads to society of crystal type, since agents sacrifice some part of individual

preferences in favour of joint preferences of the society (nonlinearity).

2. Consider a community of farmers-landowners. When land slots are fixed by law

(inheritance, etc), there no room for conflicts. Endogeneous cooperation can emerge

in sharing machines, due to scale economies.9) Here we have mixed effect of spatial

economics and nonlinearity.

3. The balance between increasing returns to scale and transport cost in the

environment of consumers spread over space can lead to emergence of optimal

spatial structures, which are vulnerable to the change of external parameters, like

world price for energy or transport cost; see Yegorov (1998, 2005a).

4. Invisible hand is also responsible for emergence of order, and this is done by

neoclassical microeconomics. However, some equilibria are not robust or

dynamically unstable, and thus they are not considered in dynamic framework.

4. Role of Analogies of Temperature and Pressure in Society

Thermodynamics is one of branches of physics that is formally close to economic theory.

Contrary to many “open branches” of physics that are not formalized axiomatically and

develop together with new empirical findings, thermodynamics is deduced from a set of

axioms and thus formally resembles the building of contemporary economic theory.

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8) Newton’s law has inverse first power for potential, and inverse second for a force; economists more

often use inverse first power.9) This case was observed in 1920s in Soviet Union, after revolution and before collectivisation,

which has not been endogeneous formation of cooperatives but too rapid process influenced by

external force.

However, there is an important difference in one property of studied processes.

Thermodynamics studies irreversible processes. They are different from those in Newton

mechanics, because at macro level (and thermodynamics formally deals with the

properties of large groups of molecules, although a formal link between micro and macro

levels is studied by statistical physics) time in physics becomes irreversible.

For microeconomic theory this question is irrelevant, since it typically abstracts from

dynamic processes. However, even if it would do dynamics (like macroeconomic growth

models, for example), the principle of equilibrium would put important limits to the set

of studied questions. In thermodynamics and statistical physics only a class of adiabatic

processes (infinitely slow) is reversible.

But the main goal of this section is different: it is related to finding the analogies

between some macro variables in thermodynamics and in social science.

4.1 Analogies

In physics, temperature T represents one of the parameters responsible for different states

of matter as well as phase transitions between them.10) Temperature of gas is related to

the average energy of molecules. The increase of temperature leads to the transition from

solid state to liquid, and later to gas and plasma.

The second parameter is pressure p. If temperature is kept constant, the decline of

pressure works in a way similar to temperature increase.

The thermodynamic state of gas in a fixed volume V is described by the law of Boyle-

Mariott: pV�Tc, where c is constant for fixed mass and chemical composition: c�Rm/m .

The average kinetic energy, K, of molecules in gas is much higher than potential energy

of interaction, ∏: K/∏��1. For liquid, they are of similar order, while for solid state the

relation is reversed: K/∏��1.

Low temperature and high pressure create crystals with long-scale order. High

temperature and low pressure create gas with no order, practically chaotic motion. Liquid

is an intermediate stage, while liquid polymer is a particular case of rather complex chain

structure.

Now consider social analogies. Temperature is an analogy of economic wealth w,

while inverse pressure is an analogy of economic freedom, f.11) The increase of wealth

and individual freedom should lead dictatorship to democracy through a chain of


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10) In fact, this is a general philosophical law of transformation of quantitative change into qualitative

change, discovered by Hegel.11) While it is difficult to propose quantitative formula for economic freedom, it is clear that one is

higher in democratic society than under dictatorship.

intermediate states. There is an analogy between dictatorship and solid state, and

between democracy and gas. For dictatorship, the ratio of individual energy to social

energy (measured for example, as the share of freely disposable income in per capita

GDP) is low, while for democracy it is high. Another prediction based on physical

analogy is that democracies should be richer societies than dictatorships.

4.2 Solid, liquid and gas-type societies

In nature we have a variety of different chemical substances with a common property: to

be sequentially in solid, liquid and gas states depending on temperature and pressure.

The trip of “Voyager” towards giants of the Solar system has discovered different

substances on different planets to be in states different from those on the Earth. This is a

collective interaction of identical elements, that gives rise to different states under

different external conditions. Although the similar theory of society is currently absent,

economic models involve representative agents which to some extent are analogies of

atoms or molecules.12) We observe societies (also in historical retrospect) with different

level of individual freedom. In dictatorships we have low level of individual activity in

comparison to social; these are “solid” societies. Fully liberal societies (where the role of

state can be asymptotically neglected) have unrestricted individual activity, and all

equilibria (at least in neoclassical economic models) emerge under this assumption.

The intermediate case corresponds to “liquid society”. In physics, liquid is

characterised with low-distance order and long-distance disorder. Models based on local

interaction satisfy this property. This is also similar to economics of networks, which is

now becoming increasingly popular. Liquid society may contain spontaneously emerging

chains of polymers.13) It usually takes place in moderately rich societies with some

degree of individual freedom. Strong state and little individual wealth prevents this state

from emergence. Mafia, at least in the sense of unofficial power different from state,

usually do not emerge in very poor and very rich society, and when state is extremely

strong.

Interaction between agents of different types can be neutral, positive or negative. In

the paper by Aruka and Mimkes (2006) six real structures of agent interaction are

introduced: segregation, aggression, partnership, hierarchy, democracy and global

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12) The economic concept of agents does not specify whether agent can be given by individual,

household, firm, etc. Usually it assumes that agents are identical, which suggests that individuals are

considered. It is also problematic to talk about unique utility for a group of agents. That is why

economic individuals resemble atoms in physics, while household–molecules.13) Examples of these polymer structures contain mafias and clans.

structure. Classical economics deals more with either no interaction (everybody

maximizes own utility, gas-type society) or negative interaction (an attempt to gain at the

expense of partner is common in games considered by economists). It is important to

mention that a theory of positive interaction (altruism) is also finding its way among new

trends of economic theory (see Bowles, 2003).

5. Extensions of Neoclassical Economics: Mathematical Formalization

5.1 Post-Liberal Economics: Necessity to build a link between main

fundamental ideologies

Globalisation process sets forward a problem of coexistence in the world with

different ideologies. In order to understand how multiplicities of social structures can

coexist, interact and transform into each other, it is necessary to have common language

for expression of global states of economy. Especially this was important before

transition. How was it possible to talk rationally about it, if there was no economic

language to describe transition path (it started in one society and had to end in another)?

Contribution to political science is also on agenda. This section aims to introduce some

mathematical elements of formalization of the problem.

Bowles and Gintis (2005) show that it is difficult to sustain cooperation in n-person

public good games, like food-sharing, co-insurance, common defence, information

sharing, by means of standard tit-for-tat and other reciprocal strategies. The

contemporary study of human behaviour has documented a large class of social

behaviours inexplicable in terms of reciprocal altruism. Laboratory and field experiments

show that other-regarding preferences cause robust cooperative behaviour, even in

anonymous setting. These finding put the investigation of non self-regarding preferences

into the agenda. Almost all microeconomic textbooks (with a nice exception of Bowles

2003) exclude them from consideration.

The link between a dominant economic theory (neoclassical economics) with the

ideology of liberalism is obvious, but is not discussed by economists. While Marxism

was the major ideology for substantial part of the world during several decades of the

20th century, there was no attempt to translate its paradigms into mathematical language

and to compare them with those from neoclassical economics. Here it is important to

make a distinction between works of K. Marx and Marxism as one of important

ideologies. In its practical implementation (Soviet Union, Eastern European countries,

China) it lead to low income dispersion and caring about the utility of the poorest

members of the society. This section aims to suggest a direction in mathematical


– 157 –

economics, along which such a link can be done.

5.2 Preferences

Despite significant ideological difference with neoclassical economics (and not less with

Marxist or other alternative), I will follow the formal canons of neoclassics and start with

assumptions and mathematical formulations.

In order to cross the natural border of neoclassical economics and to build a formal

link with formal economics, describing alternative social structures (nationalism,

Marxism), it makes sense to extend individualistic utility function, in order to capture

some altruism, or care about social utility. The social welfare functions are studied in

public economics and normally include a wide spectrum of utilities formally captured by

the formula

(1)

where a�[0,1]. In the limit case, a�1, we get utilitarian social indifference curve:

. Without special justification at the moment, we will consider this

social utility to correspond to nationalist society. Consider as an alternative Rawlsian

social indifference curve, formally given by the wealth of the poorest member of society:

Usoc|a�0�miniU0,i. This concept is very close to Marxian paradigm, since in this case

equalization of income of all members of society brings the highest social welfare. The

basic difference of nationalist society from Marxist society is that wealth inequality in

nationalist state does not generate envy, and all agents are better off if some members of

their nation become richer. The next step is a formal link between individualistic and

social theories. Let us make formal assumptions.14)

Assumption 1

Individual utility in a nationalist society is a weighted sum of own utility plus the sum of

utilities of all members of the nation:

(2)U U Ui i i

j

� �0 0, , .β∑

U Usoc a i

i

| ,� �1 0∑

U Usoc ia

i

a

� 0

1

,

/

,∑

Y. YEGOROV

– 158 –

14) These assumptions assume some level of altruism which is also studied by economists. We do not

focus the attention here on the extent of this altruism (family level, nation level or global level). Every

level can generate some structures of different order, and we focus on a country level only in order to

use minimal mathematical complexity.

Assumption 2

Individual utility in Marxist society is given by another weighted sum:

(3)

Corollary 1

Both nationalist and Marxist societies, in contrast to liberal individualistic society,

assume some level of altruism, since b�0.

Corollary 2

These utilities allow for some (nonlinear) interaction between members of the society,

which normally15) gives rise to spontaneous emergence of some state-type structures,

which can become a separate subject of action and not necessarily act in line with the

preferences of all society members. On the other hand, liberal principle, under certain

condition16) considers state as something external, destroying Pareto optimality which

spontaneously emerges on liberal market.

Corollary 3

The distribution of wealth matters for both nationalist and Marxist societies, while it

does not matter for liberal society, because the latter has no nonlinearities in market

interactions. This issue will be studied further.

This is only the first step of mathematical formalization. It is based on existing

concept of social utility (see Stiglitz, 1988), introduction of second dimension in

individual preferences (idea of McClintock (1978)) and coexistence of three main

ideologies (liberalism, nationalism and Marxism).

We can see that neoclassical economics based on liberal principles is an asymptotic

limit of nationalist or Marxist society, for b→0. It shows also why altruism is not

included in neoclassical agenda: it gives rise to spontaneous emergence of state-type

structures through preferences. But historically one can deal with existing state. One can

remember how aggressively the state was destroyed in the former Soviet Union: before

1990 it controlled the production of almost all output, while in 1999 the state controlled

less than 20% of GDP, which was an overshooting not only with respect to EU countries

(with about 50%) but also USA (with about 30%).

5.3 Scale economies and externality effects

The emergence of stable structures in physics occurs through potential of interaction.

U U Ui ij

j� �0 0, ,min .β


– 159 –

15) This is a result of synergetics.16) No externalities, perfect information, etc — see Stiglitz (1988) for details.

Generally, the energy of the system is not equal to sum of energies of separate parts but

is given by:

(4)

The difference represents interaction. In economic language, it is externality. Economic

models are mostly linear, i.e. they ignore interaction potential. The theory of firm in its

part related to its spontaneous emergence, is not a part of modern economic theory. But it

is clear that externality effects play role here.

Externalities for labour

Consider a production function with labour being the only input: Y�f(L). Since labour is

not infinitely divisible, consider self-employment as a firm with minimal quantity of

labour. If technology is such that joint productivity of 2 workers is higher than sum of

their productivities if they work separately, Y(2)�2Y(1), we have positive externality, or

increasing returns to scale (IRS) effect to labour input in technology, and thus a potential

for cooperation. As is shown in Yegorov (2001b, 2005a), the distribution of output for

this technology is not obvious, and there may be contradictions between individual and

group goals if we base conclusions on standard microeconomic principles. Modern game

theory focuses too much on the bargaining problem. It makes sense to consider the case

when bargaining would not emerge at all, i.e. individual optimisation will coincide with

group optimisation. But if preferences are altruistic (of type (2)), there might be some

range of parameters b so that there is no contradiction.

Externalities for capital

Now consider a technology with capital K as unique input. Assume that agents’

individual wealth, W, is an upper limit for capital that they can use for investment.

Consider technology Y�g(K), with g of IRS-DRS type. Then, at some level of K�K*,

the average capital productivity Y/K is maximized. If the total capital in society with N

agents is KN, then it is socially optimal to split it into M firms, each of size K*�KN/M.

Now consider individual investment decisions. For low W, several agents need to

cooperate to start a firm with K*. In a rich society individual may own a firm.17) If wealth

grows, less cooperation is required, and society becomes more atomised. This is

completely in line with the discussion about the role of temperature in society provided

above.

E system E Ei

i

( ) ( ).� � interaction∑

Y. YEGOROV

– 160 –

17) This is more applicable for agriculture, with small farms, and necessity to cooperate for poorer

people.

5.4 Local cooperation leading to emergence of ethnic group

The role of altruism in preferences is important for many reasons. Some of them have

been discussed in the book of Bolwes (2003). Here an example is provided. It has two

goals: a) to demonstrate that altruism can bring more stability to the concept of equilibria

and to lead to more robust structures, b) to explain possible mechanism of emergence of

ethnic group.

The idea of the model is based on the stylised fact about cooperation inside local

communities, along to their suspicion to a stranger. The border of a community may be

different: some people put it on a broad family, some on nation, there also exist

internationalists, with altruistic attitude towards all human beings. It is clear that

altruistic component plays an important role in such formations, as well as the link

between nation and particular area on geographic map. The goal of this model is to

propose a procedure leading to an emergence of such structures.

Consider uniformly populated landscape, where agents can be put on a lattice (in

discrete model) or occupy the space with a uniform population density. Two-

dimensionality and geographical relief are not very important at this stage. Thus, it is

assumed that agents live on a line, each occupying a particular location x. Geographic

dimension is not a unique dimension in this model. Assume also cultural difference

(language, habits, traditions, religion), measured by a function h(x), which is assumed to

be slowly varying with spatial coordinate: |h�(x)|��1.

Local interaction and altruism

In order to model interaction, we assume that initially agents are playing prisoner’s

dilemma game with their neighbours. The payoffs are given by the matrix18) (Table 1):

This game has bad (not efficient) Nash equilibrium (1, 1) in a standard framework of

preferences.

Now assume that both agents value not only their utility Ui, but utility of their partner

as well (Table 2):

Table 1. Game for U

L R

U (3, 3) (0, 4)

D (4, 0) (1, 1)


– 161 –

18) The payoffs are chosen just for illustration

V1�U1�aU2,V2�U2�aU1, (5)

where a�(0,1) — coefficient of altruism. The new game for V is given by the following

table of payoffs. Depending on a , we can get a shift to more efficient equilibrium UL.

We need a�1/3 to have such a shift.

Radius of cooperation

Let us assume that the level of altruism depends negatively on total distance between any

pair of agents,19) d�d12�mDx�Dh. This can be a combination of geographical and

cultural distances. Historically, people did not move a lot,20) and geographical proximity

implied cultural and religious proximity. Suppose that a�1/(1�d ). Then for d�(0,∞)

we have a�(0,1). We immediately arrive to spatial pattern of cooperation. In our game

people with distance d�d*�2 would select efficient equilibrium. Translation into

normal language would mean that “local communities play games cooperatively across

them, but may be noncooperative with strangers”. This behaviour can be easily observed

in some modern cultures that have kept traditions (Greece or Japan, for example).

So far, we have explained why an agent would treat his local community better than

strangers. But we have not explained, how nations, with much higher radius of territorial

distance (R��d*), would form a cluster of cooperation. We need to describe the

mechanism of spatial propagation of local interaction, which at the same time ends at

some border. Such borders are usually determined by either language or religious

Y. YEGOROV

– 162 –

19) Here m�0 is a parameter, which can be used for setting different weights for geographical and

cultural differences.20) In the sense that a small fraction of population migrated on long distances during their lifetime.

Only recently overall migration increased significantly.

Table 2. Game for V

L R

U (3(1�a), 3(1�a) ) (4a , 4)

D (4, 4a) (1+a , 1+a)

differences.21)

Travellers

Now assume that agents can travel, but their frequency of travel declines with distance

exponentially. In other words, his probability to play a game with an agent at the

geographical distance x is P(x)�le�l ,x. Such a specification satisfies the necessary

condition for probability distribution: ∫0

∞P(x)dx�1. At the same time we will consider

factor m to be a small parameter: m��1. In other words, agents almost neglect

geographical distance and look only at cultural. Still, we cannot take geography out of

the model, since it defines the pattern of travel. We also assume that initially agents were

grown in a cooperative neighbourhood and got used to it when they became adults and

started to travel. Finally, we assume that agents cannot measure cultural difference

before interaction but can observe it through response. They can adapt their behaviour in

two ways: a) they reverse cooperative to non-cooperative behaviour, if the payoff (in V!)

becomes smaller than for alternative strategy; b) they travel less frequently to the

direction where they have observed non-cooperative behaviour.

Propagation of cooperation in space

Without focusing on initial emergence of cultures and languages, we will consider spatial

heterogeneity, characterized by function h(x), as given. Clearly, it has areas of slow

variation (dialects, for example) and sharp borders, where transition occurs over small

geographical distance Dx. Define the area with no sharp differences in culture as pre-

nation area. As people increased their mobility (and this happened historically with the

development of transportation), parameter l declined. Agents started to cooperate in a

broader neighbourhood, and they did not learn to reverse their behaviour unless they

lived close to cultural border, and had high fraction of communications with different

culture, which has resulted in suboptimality of cooperative behaviour. By learning to

move there less frequently, they managed not to reverse initial strategy of cooperation,

which finally has covered all pre-nation area. This is how nations could have formed.


– 163 –

21) Holland and Belgium represent a good example. Belgium is not homogeneous, with Flemish

(almost Dutch) language spoken on the North and French in the South. At the same time, it is

religiously more unique, since the border between Catholic and Protestant religions approximately

coincides with the border between two countries. This shows more important role of religion in

comparison with language, in defining historical borders of a country. However, often the difference

of only one factor is sufficient for separations. We can observe a variety of languages and religions

inside one country for former empires, which worked as an external force to put together communities

that would segregate otherwise.

6. Applications

The goal of this section is to describe the directions where this philosophy of research

can be applied. It is impossible to predict now all fruitful applications, but it makes sense

to mention some of them. Some elaboration is done with the concept of wealth

distribution and stability conditions for liberal society. The final subsection tries to bring

some structure and interlinks between areas of research.

6.1 Where these models can be useful?

Here the short agenda of interesting directions of future research is listed. It is believed

that these social processes can be properly described by the methods discussed in this

article. However, further elaboration can take substantial effort and time, and thus could

be an agenda for future research.

1. Analytical description of transition process. The transition from centralized to

market economy in the former Soviet Union started in 1992 with “shock therapy”.

In the press it was argumented by welfare theorems from neoclassical economics

about efficiency of emerging market equilibrium. However, the concepts of that

theory were not applicable not only because lack of knowledge, lack of

institutions, incomplete and asymmetric information (especially in the case of

privatisation), but also because the transition itself is a disequilibrium process

(and fast, shock, non-adiabatic transition especially) by definition, and the western

economic school has never developed such disequilibrium theory. The use of

some tools from physics allows to do this in principle, and although it is too late

to apply results practically, this could be an important contribution to our

understanding of modelling real economic processes.

2. Explaining historical paths of different social formations.

3. Understanding the stability of different regimes and seeing economic reasons

behind it (a self-reinforcing loop: poor society tends to be a dictatorship which

keeps it poor) and their right to exist.

4. Studying the role of state in economy and its link to level of freedom and

richness.

6.2 The role of wealth distribution

It is possible to predict the crucial difference between Marxism and nationalism, arising

from the effect of wealth distribution. Empirically we know that nationalist or religious

societies are much more tolerant to wealth inequality than those based on Marxist

Y. YEGOROV

– 164 –

principles. But the structure of formulae in Assumptions 1,2 give exactly the same

predictions. Suppose that wealth is distributed not equally but there is no way for

costless redistribution. Then such redistribution would mean some decline of the second

term in utility function of each member. For some members, non necessarily rich, but of

middle class, this decline will overweight potential personal gain. Thus, a majority

interested in such redistribution will not emerge. Consider now Marxist society. For it,

any deviation from equality brings negative utility to each member. Suppose, for

simplicity, that there are two levels of wealth: low w (fraction a) and high w (fraction

1�a), where a�(0,1) but most likely to be closer to 1. Then the utility of poor is

Up�U0(w)(1�b), while the utility of rich is Ur�U0(W)�bU0(w). For b high enough,

even richer people would be personally interested in full equalization. Alternatively, for

low b two classes will emerge, with all consequences predicted by Marxists. In the case

of general distributions it is likely that low inequalities will not generate antagonism is

either society, while for higher level, nationalist society is more tolerant and stable than

Marxist.

6.3 The conditions of stability of liberal society

While it is difficult to criticize the principles of liberal society (freedom, equality,

brotherhood), its realization is often far from proclaimed principles.22) Usually liberal

society self-reinforce the initial difference in endowments and skills among agents.23)

The main reasons involve asymmetric access to credit (the rich can get it always and at

lower interest rate than the poor) and more destabilizing effect of random shocks on

households close to subsistence level. Thus, liberal principles does not guarantee “honest

outcome” when every worker gets wage according to his productivity, and everybody

can be an entrepreneur, with outcome depending on skills only.

The natural political principle of liberal society is the majority voting scheme, with the

main focus on median voter. Now let us turn to the physical principle of phase transitions

described before. Suppose that the initially high role of state in relatively poor country

was forcefully diminished, like it happened in Russia in 1990s. The liberalization has

caused wealth polarization.24) If Marxist ideology had not been rapidly abandoned, this

could have lead to emergence of classes with their struggle. The main ideological


– 165 –

22) As well as realized societies based on Marxist principles.23) The polarization across peasants initially endowed with almost equal slots of land after Russian

revolution of 1917, by the year 1930.24) I am not mentioning the increased role of mafia as another natural consequence of the decline of

state role.

competition was between nationalist and liberal idea. Consider the conditions for liberal

paradigm to win this competition. The median voter was objectively worse off

economically.25) With a monthly average income of about 100 USD and almost western

prices (despite huge temporal variation of nominal average income in Russia between

1993–1999, the PPP adjusted income did not change much.) At such income level, gain

from less pressure (more freedom) did not compensate for economic loss, and the

composition of these two parameters naturally corresponded to “solid” or “liquid”, but

not “gas” state. The richer 10% were naturally supporting “gas” (liberal) state, but they

needed to use some manipulation of public opinion with mass media, to form an illusion

of social agreement on liberal state. On the other hand, the increase of nationalistic ideas

and the role of religion worked towards higher popularity of nationalist (solid) state

among medium voters. Since “solid” and “gas” state cannot coexist (while solid and

liquid can), some liquid (better to say, polymer) structures have started to emerge in

business. They can be formally studied by economics of networks.

6.4 Link with research on structural economics, science of transition and

political science

In order not to get lost in the variety of fundamental cornerstones of future econo-physic

theory and variety of its applications, it makes sense to impose some preliminary

structure.

Structural economics

Structural economics is one of the corner stones of this new theory. It studies self-

emergence of structures in a form of spontaneously united group of agents, or network

(with or without topology of interlinks). Space is an important but not unique factor of

self-organization (Yegorov, 2001a), which also comes from nonlinear interaction of

initially identical elements (for example, through production function, locally having

IRS; see Yegorov (2001b, 2005a).

Economics of transition

To study economics of transition theoretically, one needs a formal link between different

regimes first. The proposed utility function and the analogies of phase transitions in

physics represent one possibility to build such models. Modelling transition is a

fundamentally difficult task. While transition in a narrow sense (as shift of capital and

labour to new sectors during industrialization) can follow an optimal path, transition of

Big Bang type is unpredictable in details in principle. In the chapter 8 of Faber et al.

Y. YEGOROV

– 166 –

25) By observations, only about 10 % of population had economic gain from transition, although the

majority recognize the gain in individual freedom previously suppressed by state.

(1996) the model of Big Bang, describing the behaviour of universe in the first few

seconds after its emergence, is discussed. It is fundamentally unpredictable process, as

even some fundamental physical constants could take different asymptotic values

depending on the path of the process. Transition from post-communist to market

economies included simultaneous shift in ideologies, changing of legal structure,

privatisation, mostly on the background of hyperinflation. There have been many

unpredictable novelties, and the complexity is likely to be of higher order, than simple

multiplicity of equilibria. It could also involve a sequence of unforcastable structural

changes along the path of convergence to new equilibria. While it is generally

impossible to describe this process mathematically as a deterministic path, the

application of some evolutionary concepts is important in understanding its structure.

The concept of self-emergence of structures and their stability is as important as the

concepts of “genotype” and “ecological niche” in theoretical biology. But obtaining

unified mathematical model, that is able to describe the social system dynamics both is

non-liberal and liberal framework, which was discussed above, is of crucial importance

before any practical modelling takes place.

Political science

The emergence of stable structures and studying the limits of their stability can give

some insights for policy makers. If a particular state is natural, no external reforms can

change its structure in the long run. “Heating” society involves both the decline of the

state role together with wealth increase (external aid). For example, decline of state’s

role without significant increase of wealth of median voter, cannot assure a foundation

for a stable democratic society. And the example of Russia (where an attempt to

compensate the lack of aid by excess destruction of state, which did not finally succeed

in establishing stable irreversible democracy), in contrast with Eastern and Central

European countries,26) is a good illustration.

6.5 About social diffusion, vertical and horizontal

Let us start from physics. Diffusion is the process of penetration of elements of one

nature into the media of different nature. For example, two gases were separated and

now they are in contact. Molecules of one of them will penetrate into the other. The

process of diffusion is described by diffusion equation, which shows that the total

amount of penetrated molecules and the average distance of penetration grow over time

but non-linearly. The situation with liquids is different. If we have a mixture of different

liquids with different densities, their location is ordered with time. This principle is used


– 167 –

26) I mean mostly Hungary, Poland, Czech Republic.

in rectification columns to separate oil into fractions. If we mix oil with water, it will

occupy the upper part of the volume in gravity field. The reason that prevents diffusion

in the case of liquid is related to the interaction field between the molecules of the same

type: other molecules do not allow one molecule to escape, we have some kind of

collective phenomenon.

Can we find interesting analogies in social life? Yes. Let personal wealth be an

analogy of individual energy, while the interaction forces are represented by some formal

and informal laws (traditions, collective rules, etc). If these forces are weak, we have

liberal society (an analogy of gas), but if they are strong, we have a traditional society. In

traditional societies it is difficult to make an action without mental self-reference to the

opinion of collective, while in liberal societies individuals are independent on this

opinion.

Consider the process of mobility across social classes. In traditional society, a person

without proper genealogy could not become an aristocrat, independently on the level of

his wealth. This was the reason of bourgeois revolutions, which improved social status of

the “third class”. In modern liberal societies, entry to another social group is more easy,

but we also have some “closed societies”, a ticket to which cannot by bought. The

described case is an example of vertical social diffusion, which is more easy in gas-type

(liberal) society and more difficult in liquid-type (traditional) society.

Another example is related to horizontal diffusion, and it can be easier explained using

military example. In the time of the Second World war the fronts separating two armies

were well defined in space, and penetration (diffusion) was a difficult task, at least at

mass level. Now, in the epoque of terrorist attacks, such diffusions play an increasing

role in the strategy of a conflict. The previous society was more of liquid type, with more

control over actions of each individual, while now societies are more liberal, and this

control became less. Gas-type diffusion in modern societies became easier for

individuals. The examples considered above show how the analogies between physics

and social life can be used for studying particular questions of social organization and

movement.

7. Conclusive Remarks

The method of introducing physical methodology into economic modelling with keeping

most of economic assumptions allows to describe much richer class of socio-economic

phenomena. In particular, it is possible to deal with emergence of different structures and

study different social orders by common mathematical tools. This paper only sets up

Y. YEGOROV

– 168 –

some potentially fruitful directions of research.

It is shown that market force in not a unique interaction between economic agents.

Non-market interaction include deviation from self-regarding preferences that can

explain the emergence of stable structures (like groups, nations and countries).

Moreover, movement along these lines allow to explain the societies based on alternative

ideologies (Marxism and nationalism).

Spatial forces represent another self-organizing social principle that is complementary

to “invisible hand”. This explains the importance of regional science and urban

economics. Scale economies can also lead to endogeneous group formation. In

combination with transport costs they give rise to a wide range of stable heterogeneous

structures in space.

The analogy between different phases of matter (solid, liquid, gas) and social orders

with different levels of economic freedom is presented. It allows to provide a wider view

on possible socio-economic structures and the order parameters (social analogies of

temperature and pressure from physics) that are responsible for phase transitions

between them.

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Econo-Physics a Perspective of Matching Two Sciences

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