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PHYSICS REPORTS   (Review Section of  Physics Letters) 204,   No.   1(1991)1—163. North-Holland

PHYSICS   AND SOCIAL   SCIENCE - THE APPROACH   OF   SYNERGETICS

Wolfgang   WEIDLICH  Inst itut  für  Theoretische   Physik,   Universitbt Stuttgart, Germany

Editor:   B.   Muhlschlegel Received   September   1990

Contents:

Introduction   3   4.5.   Probability   distribution  and   stochastic  trajectories   51

1 .   Comparison of  structures   7    5.   Collective   opinion formation   53 1.1.   The  level structure of nature and  society   7   5.1.   The   two-opinion case   54

1.2.   The   interaction between   levels:   the   “reductionist”   5.2.   Dynamics of  party   images and  voters   opinions   in  the

versus   the   holistic” view   9   democratic   system   69 1.3.   Quantitative  modelling   in   social   science   12   6.   Migration   of  populations   77

2.   Interaction   of   macrovariables  — semi-quantitative   consid-   6.1.   Comparison   of  migration   and   opinion   formation   77

erations   14   6.2.   The   migratory  equations  of motion   78

2.1.   The   macroscopic  approach   14   6.3.  The   case of  two interacting   populations   81

2.2.  An abstract   metamodel   describing   stability   and   cy-   6.4.   Deterministic   chaos   in   migratory  systems   92 clicity   14   6.5.   Empirical  evaluation   of  interregional migration   95

2.3.   Selected examples of  model   interpretation   23   7.   Formation   of settlements   10 9

3.   The framework  of   microbehaviour and  macrostructures   25   7.1.   Master equation   description  of urban evolution   on  the 3.1.   The   space   of   social structures— aspects,   issues   and microscale   11 0

attitudes   25   7.2.   Migration   and   agglomeration on   the macroscale   12 0 3.2.   The   variables: socioconfiguration, associated  variables   7.3.   Settlement  formation   on  the mesoscale:   an integrated

and   trend   configuration   27   economic   and   migratory  model   13 1

3.3.   The   elements of   sociodynamics: dynamic utilities  and   7.4.   Alternative  approaches to  urban   dynamics   14 1

probability   transition  rates   30   8.   Master equation approach   to   nonlinear   nonequilibrium

4.   Constitutive  equations  of  motion   34   economics   14 6

4.1.   The  master equation   for   the   socio an d   trend   configu-   8.1.   Introductory remarks   14 6 ration   36   8.2.   Modelling concepts:   the  economic configuration   and

4.2.   Mean-value   equations  for the components of the   socio   the  elementary  dynamic processes   14 8

and   trend   configuration   38   8.3.   Master equation   and   mean-value   equations   for   the

4.3.   Stationary   solutions   of the   mean-value   and   master   economic   evolution   15 2

equations   41   8.4.   Analysis  of market   instabilities   15 4

4.4.  A   special   time-dependent   solution   to   the   master References   16 2

equation   47

 Abs tra ct:

Universally applicable methods   originating in   statistical  physics an d   synergetics are  combined with  concepts from social  science in  order to set up and   to   apply  a  model   construction concept   for   the quantitative  description  of a  broad   class of  collective dynamical phenomena   within   society.

Starting from the  decisions of  individuals and  introducing the  concept of  dynamical utilities,  probabilistic   transition  rates between attitudes and

actions   can  be  constructed.  The latter enter the central   equation  of  motion,  i.e. the   master   equation,   for   the  probability   distribution   over the

possible macroconfiguration s of   society. From   the master   equation   the  equations of  motion   for   the   expectation   values  of the   macrovariables of 

society can   be   derived. These equations   are   in   general nonlinear.  Their   solutions   may   include stationary solutions,   limit   cycles   and   strange

attractors,  and  with   varying trend  parameters   also   phase   transitions  between different modes  of  social behaviour   can  be  described. The   general  model   construction   approach   is   subsequently applied   to   characteristic   examples from   different  social  sciences, such  a s   sociology,

demography,   regional   science and   economics.   These   examples refer   to   collective   political   opinion   formation,   to   interregional   migration   of 

interactive  populations, to  settlement formation o n   the micro-,  meso- and  macroscale, and to  nonlinear   nonequilibrium economics, including  market

instabilities.

0   370-1573/91/$57.05  ©   1991   —   Elsevier  Science  Publishers  B.V.   (North-Holland)

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PHYSICS   AND   SOCIAL SCIENCE   - THE   APPROACH   OF   SYNERGETICS

Wolfgang WEIDLICH

 Insti tu t   für  Theoretische  Physik,   Universitàt  Stuttgart,   Germany

I NORTH-HOLLAND

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W .   Weidlich,   Physics and   social  science  —   the approach   of  synergetics   3

Introduction

In   the   last   20   years   great   progress   has   been made in understanding   complex systems  in   physics,

chemistry and biology.  The   new  concepts  necessary for this understanding were  primarily developed in the   statistical  physics of open   systems far from  thermodynamic equilibrium and in  fields   like  quantum

optics and the theory of  chemical   reactions, where new   types  of  “nonequilibrium dissipative structures”(using  the nomenclature of I.   Prigogine)   appear. The   conceptual framework  for the   mathematical   treatment   of   such   systems   finds  a  rather  general

formulation   in   “synergetics”,   by   definition,   the   science  of the   macroscopic   space—time structures   of 

multi-component   systems with   cooperative   interactions   between their   units.   The   framework   of  synergetics has   been set   up  and worked out  since   1970,   mainly by  H.   Haken [1,  2 1 .

It   is   the purpose of this   article   to   give   an   account   — in   view  of these   developments   in   natural science   — of   new   approaches   to make methods of   statistical   physics   and   synergetics available   and transferable to a  quantifiable description of   dynamic  processes   in   human  society.

In   doing so, we are not   aiming to present an uncoordinated collection of quantitative   treatments of  sectors of   society.   Instead,  our intention   is  more  systematic.   W e   will   try to   set up   a general   “model

construction strategy” for a   quantitative  — or at   least   semi-quantitative   — treatment of  a whole   class  of  macrodynamic   evolutions   in   society, making   use   of   those   concepts   of   statistical   physics,   whose relevance   is  not  only  particular to  physics but   is   much more   universal!

However,   since   the   article   is   primarily written for   physicists,   we   will   also   make   side   remarks whenever structural   analogies   between   physical   and   social systems   appear and seem   worthy   of  consideration.   It is  our hope that the   interdisciplinary   relevance of  some concepts   of   synergetics  can  be demonstrated   in  this way,  and that the approaches  developed  here contribute to the idea of the “unity

of  sciences”. For   two   decades the author of this article, being a theoretical   physicist, has been   engaged   with

increasing intensity in the problem of a   quantitative description   of  the   dynamics of  social  systems.   Some of the  main results of this research,  obtained in  cooperation with  a small   but highly   motivated group  of  physicists,   are   summarized here   (cf. the   acknowledgements).

The  work in the   new   field has  also  led, due to their  gratefully acknowledged   open-minded  attitude, to new  contacts and even to  close cooperation with social scientists.   In this context  a special observation under the   perspective of a   physicist should  be   made:

Physicists   are   used   to a thoroughgoing mathematical  quantitative  fonnulation of their theories and consider   qualitative argumentations only  as a  preliminary  stage   of  theorizing  about phenomena. On the other hand, the  mainstream   of  social   science   — with   the exception  of  economics   — concentrates   on   and prefers a qualitative  argume