Dynamical Economic model in a finite world Christophe Goupil1, Eric Herbert1, Yves D'Angelo1, Quentin Couix2

1DyCoE Team, Laboratoire des Energies de Demain, LIED, UMR 8236, Université Paris Diderot2 Université Paris Sorbonne

Ecoles des Houches 10 mars 2016

christophe.goupil@univ-paris-diderot.fr

Including, or not, the ressources

Glucina et al. 2010Hall et al. 1986 Berg et al. 2015

Perpetual motion et al...

Economics

• What do we learn from mechanics?

• What do we learn from equilibrium thermodynamics?

• What do we learn from out of equilibrium thermodynamics?

• Does economics have something to do with thermodynamics?

• A model where few things matter: (conservation, friction, rate…)

Economics IS Mechanics!...............?

… and Herman Laurent wrote to Léon Walras….(about the integrability of the model)

Economics ARE Thermodynamics !............?

Equilibrium thermodynamics: Callen approach

General structure

Thermodynamics

Economics

Thermoelastic coefficients & Elasticities

Is there an Economic “material”?

Debreu: Job is done….Really?

So, in other words:

The economics "material" is defined by the laws acting on...the economic "material“

The economics laws are derived from the measurements made on the economics “material”… which is defined by the same laws…that define….

Partial conclusion

1. Economics do not have the structure of thermodynamics.

2. There is no problem with doing local optimization…until we don’t claim it is GENERAL.

3. There is no fundamental equation for the economy, nor variational principle (hopefully)

4. There is no ergodicity.

5. T, P…are emerging properties, are there any in economics?

GENERAL EQUILIBRIUM

And….Economic systems are not equilibrium systems!

Commodity space

Out of equilibrium: Schumpeter

The Roegen assumption: « matter matters too»

The far out of equilibrium assumption is ok,

but there is no need of a fourth thermodynamics principle

for matter.

Money temperature (Yakovenko 2009)

There is no problem with such a definition, but why should

we call it temperature and not simply the average value of

the money carried by agents?AND!

There is no emerging quantity

« Well-lit roads and burned bridges » (Glucina & Mayumi 2010)

"The fact that there are no known exceptions to the laws of thermodynamics should be

incorporated into the axiomatic foundation of economics."(Underwood 1989) ∙

"Real financial markets cannot behave thermodynamically" because "financial markets are

unstable, they do not approach statistical equilibrium, nor are there any available topological

invariants on which to base a purely formal statistical mechanics." (Mc Caulley 2003) ∙

"If economics is to be considered as a science-based discipline, the principles of physical

science, including the laws of thermodynamics, must be appropriately applied." (Wallace 2009)

"We need to begin to incorporate energy and entropy thinking into economics."(Kummel 2011)

The use of thermodynamics in Economics

• Conservative laws (no full substitutability)

• Non conservation of some physical quantities (utility...)

• Difference between extensive and intensive physical quantities

• Intensive physical quantities are the potentials from which we can derive forces∙

• Intensive physical quantities are the potentials that give a possible measurement of the quality∙

• There is no economic entropy but we can consider quantity and quality approach∙ (general exergy)

• Give up the full thermodynamic paradigm (Integrability, Equation of state...)

• Time does matter BUT, there is no variational principle in out-of-equilibrium systems

Time does matter: a mechanical description

Efficiency is not restricted to pure thermodynamic description.

(Hall 1994)(Odum & Pinkerton 1955)

• J. Yvon, The saclay Reactor: Two Years of Experience in the Use of a Compresed gas as a Heat Transfer Agent, Proceedings of the International Conference on the Peaceful Uses of Atomic Energy (1955)

• P. Chambadal Les centrales nucléaires. Armand Colin, Paris, France, 4 1-58, (1957) • I.I. Novikov, Efficiency of an Atomic Power Generation Installation, Atomic Energy 3 (1957)• F.L. Curzon & B. Ahlborn, Efficiency of a Carnot Engine at Maximum Power Output, Am. J. Phys. 43 (1975)• For a review, see Ouerdane et al.., Eur. Phys. J. Special Topics 224, 839–864 (2015)

Endoreversible

P

ηηCA ηCarnot

Pmax

Finite Time Thermodynamics

FTT

Odum-Pinkerton, Yvon, Chambadal, Novikov, Curzon & Ahlborn

Thot

Tcold

Work

hot

cold

in

CT

T

Q

W 1

Thot

Tcold

Power

hot

cold

in

CAT

T

Q

W

1

The position of the point on the curve is defined by the intensity parameter whichgoverns the output.

Carnot

Goupil et al. 2012

Efficiency or Power?

« More is not always better »

Irreversibilities included

Friction

Leak: natural degradation

Low friction

High friction

Source

Production

OutputDP

Sink

PR

PS

PPH

PPL

FPH

FPH

Efficiency or power : (small DP change)leakfriction

restricted access

to ressources friction + leak+ restricted access to ressources

friction + leak

Hall et al. 2006

The Lego brick

The Lego brick description

Internal parameters:

Total ressource XT

Frictions: R

Coupling terms: a

Natural recycling: FNR

Outputs:

Prod output: WPCout

Recycling flux

…

Healt parameter: M

Inputs: demands

Production (Leontief PC)

Recycling (Leontief PR)

1

2

3

4

Safe: M>>1

Max Eff: M=(1+Z)0.5

Max Prod: M=1

Unsafe: M<1

1

2

3

4

M=Rin/Rload

Complete system

Complete system (small DP change)

M1

K

M2

Smell test…

Smell test: recycling increased

Conclusions

1. Economics do not have the structure of thermodynamics. 2. There is no economic entropy but quantity and quality approaches are possible3. There is no fundamental equation for economy (hopefully)4. There is no ergodicity.5. Economic system are not equilibrium systems.

There is no problem with doing local optimization…until we don’t claim it is GENERAL.

1. Conservative laws (non full substitutable) 2. Non conservation of some physical quantities (utility...)3. Difference between extensive and intensive physical quantities 4. Intensive physical quantities are the potentials from which we can derive forces5. Give up the full thermodynamic paradigm (Integrability, Equation of state...)6. Time does matter BUT, there is no variational principle in out of equilibrium systems

• Walras 1909: Walras Léon Économique et Mécanique, Bulletin de la Société Vaudoise de Sciences Naturelles Vol. 45, p.313-3251.• Soddy 1911: Soddy, Frederick. (1911). Matter and Energy (pgs. 33-35). H. Holt and Co.• Soddy 1920: Soddy, Frederick. (1920). Science and Life, New York: Dutton.• Soddy 1921: Soddy, Frederick. (1921). "Cartesian Economics: the Bearing of Physical Science upon Start Stewardship“.• Wilson 1938: Wilson, Edwin. (1938). "Letter to Paul Samuelson", Dec 30.• Gibbs 1876: Willard Gibbs, (1876): "Internal Stability of Homogeneous Fluids as indicated by Fundamental Equations“• Samuelson 1947: Samuelson P. A . (1947), Foundation of Economic Analysis (Cambridge, MA, Harvard University Press)• Samuelson 1960: Samuelson, Paul A. (1960). "Structure of a minimum equilibrium system“• Debreu 1984: G. Debreu, Théorie de la valeur. Une analyse axiomatique de l'équilibre économique, Paris, Dunod, 1984• Schumpeter 1939: Business Cycles: A Theoretical, Historical and Statistical Analysis of the Capitalist Process, 1939• Yakovenko 2009: Victor M. Yakovenko and J. Barkley Rosser, Jour. Rev. Mod. Phys. 81, 1703.• Roegen 1971: Georgescu-Roegen, Nicholas. (1971). The Entropy Law and the Economic Process. Cambridge, Massachusetts.• Ayres 1999: Robert Ayres, The second law, the fourth law, recycling and limits to growth , Ecological Economics, vol. 29, n° 3, p. 473-483• Underwood 1989: Underwood, D. A. and King, P. G. (1989). "On the Ideological Found. of Environ. Policy", Ecological Economics 1: 324• Mc Cauley 2003: McCauley, Joseph L. (2003). "Thermo. Analogies in Eco. and Finance…" Physica A, 329 (2003): 199-212.• Wallace 2009: Wallace, Thomas P. (2009). the Dynamics of Decaying Civilizations from Ancient Greece to America (pg. 31). AuthorHouse.• Kummel 2011: Kummel, Reiner. (2011). The Second Law of Economics: Energy, Entropy, and the Origins of Wealth.• Lotka 1922: A.J.Lotka (1922) 'Contribution to the energetics of evolution'. Proc Natl Acad Sci, 8.• Odum 1955: H.T.Odum and R.C.Pinkerton (1955) 'Time's speed regulator….”, Am. Sci., 43 pp. 331—343

References

• H. Ouerdane, Y. Apertet, C. Goupil, and Ph. Lecoeur, Continuity and boundary conditions in thermodynamics: From Carnot’s efficiency to efficiencies at maximum power ,Eur. Phys. J. Special Topics 224, 839-864 (2015)

• H. Ouerdane, A. A. Varlamov, A. V. Kavokin, C. Goupil, and C. B. Vining, Enhanced thermoelectric coupling near electronic phase transition: the rôle of fluctuation Cooper pairs, Physical Review B 91, 100501 (R) (2015)

• Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Influence of thermal environment on optimal working conditions of thermoelectric generators, J. Appl. Phys. 116, 144901 (2014)

• Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, On the distinction between maximum power and maximum efficiency working conditions for thermoelectric generators, Journal of Applied Physics 116, 144901 (2014)

• Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Efficiency at maximum power of thermally coupled heat engines, Physical Review E vol. 85, 041144 (2012)

• Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Irreversibilities and efficiency at maximum power of heat engines: The illustrative case of a thermoelectric generator, Physical Review E vol. 85, 031116 (2012)

• Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Thermoelectric internal current loops inside inhomogeneous systems, Physical Review B vol. 85, 033201 (2012).

• Y. Apertet, H. Ouerdane, O. Glavatskaya, C. Goupil and Ph. Lecoeur, Optimal working conditions for thermoelectric generators with realistic thermal coupling, Europhysics Letters vol. 97, 28001 (2012)

Out of equilibrium thermodynamics references

Utility: Locally ok but is global optimization possible?

UtThe integrability question

“According to the feasibility study, it is feasible, but,According to the idiotability studies it is absolutely idiot.”

Neoclassical Economy