The European Physical Journal Special Topics

, Volume 225, Issue 17–18, pp 3091–3104 | Cite as

Entropy and econophysics

Regular Article
Part of the following topical collections:
  1. Discussion and Debate: Can Economics be a Physical Science?


Entropy is a central concept of statistical mechanics, which is the main branch of physics that underlies econophysics, the application of physics concepts to understand economic phenomena. It enters into econophysics both in an ontological way through the Second Law of Thermodynamics as this drives the world economy from its ecological foundations as solar energy passes through food chains in dissipative process of entropy rising and production fundamentally involving the replacement of lower entropy energy states with higher entropy ones. In contrast the mathematics of entropy as appearing in information theory becomes the basis for modeling financial market dynamics as well as income and wealth distribution dynamics. It also provides the basis for an alternative view of stochastic price equilibria in economics, as well providing a crucial link between econophysics and sociophysics, keeping in mind the essential unity of the various concepts of entropy.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P.A. Samuelson, Gibbs in economics, in Proceedings of the Gibbs symposium, edited by G. Caldi, G.D. Mostow (American Mathematical Society, Providence, 1990)Google Scholar
  2. 2.
    P. Mirowski, How not to do things with metaphors: Paul Samuelson and the science of neoclassical economics, Stud. History Phil. Sci. Part A 20, 175 (1989)CrossRefGoogle Scholar
  3. 3.
    R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, 2000)Google Scholar
  4. 4.
    J. Tinbergen, The Econometric Approach to Business Cycles (Hermann, Paris, 1937)Google Scholar
  5. 5.
    P. Ehrenfest, T. Ehrenfest-Afanessjewa, Bergriffliche grundlagen der statistischen auffassung in der mechanic, in Encydlopadei der Mathematischen Wissenschaften, Volume 4, edited by F. Klein, C. Müller (Teubner, Leipzig, 1911)Google Scholar
  6. 6.
    L. Boltzmann, Über die eigenschaften monocycklischer und andere damit verwandter systems, Crelle's Journal für due reine und angwandte Mathematik 109, 201 (1884)Google Scholar
  7. 7.
    J.B. Rosser, Jr., Reconsidering ergodicity and fundamental uncertainy, J. Post Keynesian Econ. 38, 331 (2015)CrossRefGoogle Scholar
  8. 8.
    R. Clausius, Über die Energievorräthe der Nature und ihre Verwerthung zum Nutzen der Menschheit (Verlag von Max Cohen & Sohn, Bonn, 1885)Google Scholar
  9. 9.
    S. Carnot, Réflexions sur la Puissance Motrice du Feu et sur les Machines Propres à Déveloper cette Puissance (Vrin, Paris, 1824)Google Scholar
  10. 10.
    P. Mirowski, More Heat than Light: Economics as Social Physics as Nature's Economics (Cambridge University Press, New York, 1989)Google Scholar
  11. 11.
    N. Georgescu-Roegen, The Entropy Law and the Economic Process (Harvard University Press, Cambridge, 1971)Google Scholar
  12. 12.
    J.B. Rosser, Jr., From Catastrophe to Chaos: A General Theory of Economic Discontinuities (Kluwer, Boston, 1991)Google Scholar
  13. 13.
    J.W. Gibbs, Elementary Principles of Statistical Mechanics (Dover, New York, 1902)Google Scholar
  14. 14.
    P.P. Christensen, Historical roots for ecological economics-biophysical versus allocative approaches, Ecol. Econ. 1, 17 (1989)CrossRefGoogle Scholar
  15. 15.
    C. Shannon, W. Weaver, Mathematical Theory of Communication (University of Illinois Press, Urbana, 1949)Google Scholar
  16. 16.
    A. Rényi, On measures of entropy and information, in Proceedings of the Fourth Berkeley Symposium on Mathematics, Statistics, and Probability 1960, Volume 1: Contributions to the Theory of Statistics, edited by J. Neyman (University of California Press, Berkeley, 1961).Google Scholar
  17. 17.
    C. Tsallis, Possible generalizations of Boltzmann-Gibbs statistics, J. Stat. Phys. 52, 479 (1988)ADSMathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    S. Thurner, R. Hanel, The entropy of non-ergodic complex systems- a derivation from first principles, Int. J. Mod. Phys.: Conf. Ser. 16, 105 (2012)Google Scholar
  19. 19.
    J. Uffink, Boltzmann's Work in Statistical Physics, Stanford Encyclopedia of Philosophy,, 2014Google Scholar
  20. 20.
    C.G. Chakrabarti, I. Chakraborty, Boltzmann-Shannon entropy: Generalization and application, arXiv:quant-ph/0610177v1 (22 Oct 2006)
  21. 21.
    H.E. Daly, The economic growth debate: What some economists have learned but many have not, J. Environ. Econ. Manag. 14, 323 (1987)CrossRefGoogle Scholar
  22. 22.
    E. Schrödinger, What is Life? The Physical Aspect of the Living Cell (Cambridge University Press, London, 1945)Google Scholar
  23. 23.
    W.P. Cockshott, A.F. Cottrill, G.J. Michaelson, I.P. Wright, V.M. Yakovenko, Classical Econophysics (Routledge, Abingdon, 2009)Google Scholar
  24. 24.
    J. Martinez-Alier, Ecological Economics: Energy, Environment and Society (Blackwell, Oxford, 1987)Google Scholar
  25. 25.
    E. Gerelli, Entropy and ‘the end of the world,’ Ricerche Economiche 34, 435 (1985)Google Scholar
  26. 26.
    W.D. Nordhaus, Lethal model 2: The limits to growth revisited, Brookings papers on economic activity 1992, 1 (1992)CrossRefGoogle Scholar
  27. 27.
    J.T. Young, Entropy and natural resource scarcity: A reply to the critics, J. Environ. Econ. Manag. 26, 210 (1994)CrossRefMATHGoogle Scholar
  28. 28.
    J.L. Simon, The Ultimate Resource (Princeton University Press, Princeton, 1981)Google Scholar
  29. 29.
    A.J. Lotka, Elements of Physical Biology (Williams and Wilkins, Baltimore, 1925), reprinted in 1945 as Elements of Mathematical Biology Google Scholar
  30. 30.
    P.A. Samuelson, Foundations of Economic Analysis (Harvard University Press, Cambridge, 1947)Google Scholar
  31. 31.
    G.F. Helm, Die Lehre von der Energie (Felix, Leipzig, 1887)Google Scholar
  32. 32.
    L. Winiarski, Essai sur la mécanique sociale: L'énergie sociale et ses mensurations, II, Rev. Philosophique 49, 265 (1900)Google Scholar
  33. 33.
    W. Ostwald, Die Energie (J.A. Barth, Leipzig, 1908)Google Scholar
  34. 34.
    J. Davidson, One of the physical foundations of economics, Quart. J. Econ. 33, 717 (1919)CrossRefGoogle Scholar
  35. 35.
    H.J. Davis, The Theory of Econometrics (Indiana University Press, Bloomington, 1941)Google Scholar
  36. 36.
    J.H.C. Lisman, Econometrics and thermodynamics: A remark on Davis's theory of budgets, Econometrica 17, 59 (1949)CrossRefMATHGoogle Scholar
  37. 37.
    P.A. Samuelson, Maximum principles in analytical economics, Am. Econ. Rev. 62, 2 (1972)Google Scholar
  38. 38.
    J.B. Rosser, Jr., Debating the role of econophysics, Nonlinear Dyn. Psychol. Life Sci. 12, 311 (2008)ADSGoogle Scholar
  39. 39.
    J.L. McCauley, Dynamics of Markets: Econophysics and Finance (Cambridge University Press, Cambridge, 2004)Google Scholar
  40. 40.
    A.J. Chatterjee, B.K. Chakrabarti, editors, Econophysics of Stock and Other Markets (Springer, Milan, 2006)Google Scholar
  41. 41.
    T. Lux, Applications of statistical physics in finance and economics, in Handbook on Complexity Research, edited by J.B. Rosser, Jr. (Edward Elgar, Cheltenham, 2009)Google Scholar
  42. 42.
    J.M. Keynes, Treatise on Probability (Macmillan, London, 1921)Google Scholar
  43. 43.
    F.H. Knight, Risk, Uncertainty and Profit (Hart, Schaffner, and Marx, Boston, 1921)Google Scholar
  44. 44.
    C. Schinkus, Economic uncertainty and econophysics, Physica A 388, 4415 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    A. Dionisio, R. Menezes, D. Mendes, An econophysics approach to analyze uncertainty in financial markets: An application to the Portuguese stock market, Eur. Phys. J. B. 60, 161 (2009)Google Scholar
  46. 46.
    B.B. Mandelbrot, The variation of certain speculative prices, J. Business 36, 394 (1963)CrossRefGoogle Scholar
  47. 47.
    L. Bachelier, Théorie de la speculation, Annales Scientifiques de l'École Normale Supérieure III-17, 21 (1900)CrossRefMATHGoogle Scholar
  48. 48.
    F. Black, M. Scholes, The pricing of options and corporate liabilities, J. Political Econ. 81, 637 (1973)MathSciNetCrossRefMATHGoogle Scholar
  49. 49.
    M.J. Stutzer, The statistical mechanics of asset prices, in Differential Equations, Dynamical Systems, Control Science: A Festschrift in Honor of Lawrence Markus, Vol. 152, edited by K.D. Elworthy, W.N. Everitt, E.B. Lee (Marcel Dekker, New York, 1994)Google Scholar
  50. 50.
    M.J. Stutzer, Simple entropic derivation of a generalized Black-Scholes model, Entropy 2, 70 (2000)ADSMathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    J.M. Cozzolino, M.J. Zahner, The maximum entropy distribution of the future distribution of the future market price of a stock, Oper. Res. 21, 1200 (1973)MathSciNetCrossRefMATHGoogle Scholar
  52. 52.
    D. Sornette, Why Stock Markets Crash: Critical Events in Complex Financial Systems (Princeton University Press, Princeton, 2003)Google Scholar
  53. 53.
    J.B. Rosser, Jr., Econophysics and economic complexity, Adv. Complex Syst. 11, 745 (2008)CrossRefMATHGoogle Scholar
  54. 54.
    M. Gallegati, S. Keen, T. Lux, P. Ormerod, Worrying trends in econophysics, Physica A 370, 1 (2006)ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    J.L. McCauley, Response to ‘Worrying trends in econophysics’, Physica A 371, 601 (2008)ADSCrossRefGoogle Scholar
  56. 56.
    A.A. Dragulescu, V.M. Yakovenko, Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States, Physica A 299, 213 (2001)ADSCrossRefMATHGoogle Scholar
  57. 57.
    V.M. Yakovenko, J.B. Rosser, Jr., Colloquium: Statistical mechanics of money, wealth, and income, Rev. Mod. Phys. 81, 1704 (2009)ADSCrossRefGoogle Scholar
  58. 58.
    F.A. Cowell, K. Kuga, Additivity and the entropy concept: An axiomatic approach to inequality measurement, J. Econ. Theory 25, 131 (1981)MathSciNetCrossRefMATHGoogle Scholar
  59. 59.
    A.B. Atkinson, On the measurement of inequality, J. Econ. Theory 2, 244 (1970)MathSciNetCrossRefGoogle Scholar
  60. 60.
    F. Bourgignon, Decomposable income inequality measures, Econometrica 47, 901 (1979)MathSciNetCrossRefMATHGoogle Scholar
  61. 61.
    E.W. Montroll, M.F. Schlesinger, Maximum entropy formalism, fractals, scaling phenomena, and 1/f noise: A tale of tails, J. Stat. Phys. 32, 209 (1983)ADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    V. Pareto, Cours d'Économie Politique (R. Rouge, Lausanne, 1897)Google Scholar
  63. 63.
    F. Auerbach, Das gesetz der bevŏlkerungkonzentratiion, Petermans Mittelungen 59, 74 (1913)Google Scholar
  64. 64.
    J. Angle, The surplus theory of social stratification and the size distribution of personal wealth, Social Forces 65, 293 (1986)CrossRefGoogle Scholar
  65. 65.
    J.-P. Bouchaud, M. Mézard, Wealth condensation in a simple model of economy, Physica A 282, 536 (2000)ADSCrossRefGoogle Scholar
  66. 66.
    A. Chakraborti, B.K. Chakraborti, Statistical mechanics of money: How saving propensities affects its distribution, Eur. Phys. J. B 17, 167 (2000)ADSCrossRefGoogle Scholar
  67. 67.
    G.K. Zipf, National Unity and Disunity (Principia Press, Bloomington, 1941)Google Scholar
  68. 68.
    D.W. Huang, Wealth accumulation with random redistribution, Phys. Rev. E 69, 057103 (2004)ADSCrossRefGoogle Scholar
  69. 69.
    S. Solomon, P. Richmond, Stable power laws in variable economies: Lotka-Volterra implies Pareto-Zipf, Eur. Phys. J. B 27, 257 (2002)ADSGoogle Scholar
  70. 70.
    H. Föllmer, Random economies with many interacting agents, J. Math. Econ. 1, 51 (1974)MathSciNetCrossRefMATHGoogle Scholar
  71. 71.
    D.K. Foley, A statistical equilibrium theory of markets, J. Econ. Theory 62, 321 (1994)MathSciNetCrossRefMATHGoogle Scholar
  72. 72.
    D.K. Foley, E. Smith, Classical thermodynamics and economic general equilibrium theory, J. Econ. Dyn. Control 32, 7 (2008)MathSciNetCrossRefMATHGoogle Scholar
  73. 73.
    M.R. Baye, D. Kovenock, C.G. de Vries, The Herodotus paradox, Games Econ. Behav. 74, 399 (2012)MathSciNetCrossRefMATHGoogle Scholar
  74. 74.
    S. Galam, Y. Gefen, Y. Shapir, Sociophysics: A new approach of sociological collective behavior. I. mean-behaviour description of a strike, J. Math. Sociol. 9, 1 (1982)CrossRefMATHGoogle Scholar
  75. 75.
    W. Weidlich, G. Haag, Concepts and Models of a Quantitative Sociology. The Dynamics of Interaction Populations (Springer-Verlag, Berlin, 1983)Google Scholar
  76. 76.
    J. Lee, S. Pressé, A derivation of the master equation from path entropy maximization, arXiv:1206.1416 (2012)
  77. 77.
    B.K. Chakrabarti, A. Chakraborti, A. Chatterjee, editors, Econophysics and Sociophysics: Trends and Perspectives (Wiley-VCH, Weinhelm, 2006)Google Scholar
  78. 78.
    J. Mimkes, A thermodynamic formulation of economics, in Econophysics and Sociophysics: Trends and Perspectives (Wiley-VCH, Weinhelm, 2006)Google Scholar

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.James Madison UniversityHarrisonburgUSA

Personalised recommendations