Skip to main content Accessibility help
Hostname: page-component-747cfc64b6-bv7lh Total loading time: 0.222 Render date: 2021-06-15T17:50:23.255Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }


Published online by Cambridge University Press:  10 April 2019

J. Barkley Rosser Jr.
James Madison University
E-mail address:


Considering macroeconomies as systems subject to stochastic forms of entropic equilibria, we shall consider how deviations driven by positive feedbacks as in a speculative bubble can drive such an economy into an anti-entropic state that can suddenly collapse back into an entropic state, with such a collapse taking the form of a Minsky moment. This can manifest itself as shifts in the boundary between the portion of the income distribution that is best modeled as Boltzmann–Gibbs and that best modeled as a Paretian power law.

© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below.


Angle, John (1986) The surplus theory of social stratification and the size distribution of personal wealth. Social Forces 65, 293326.CrossRefGoogle Scholar
Atkinson, Anthony B. (1970) On the measurement of inequality. Journal of Economic Theory 2, 244263.CrossRefGoogle Scholar
Auerbach, Felix (1913) Das gesetz der bevŏlkerungkonzentratiion. Petermans Mittelungen 59, 7476.Google Scholar
Bachelier, Louis (1900) Théorie de la speculation. Annales Scientifiquede l’École Normale Supérieure III-17, 2180.Google Scholar
Baye, M. R., Kovenock, D., and de Vries, C. G. (2012) The Herodotus paradox. Games and Economic Behavior 74, 399406.CrossRefGoogle Scholar
Black, Fischer and Scholes, Myron (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81, 637654.CrossRefGoogle Scholar
Boltzmann, Ludwig (1884) Über die eigenschaften monocycklischer und andere damit verwandter systems. Crelle’s Journal fúr due reine und angwandter Mathematik 109, 201212.Google Scholar
Bouchaud, Jean-Philippe and Mézard, Marc (2000) Wealth condensation in a simple model of economy. Physica A 282, 536545.CrossRefGoogle Scholar
Bourgignon, François (1979) Decomposable income inequality measures. Econometrica 47, 901920.CrossRefGoogle Scholar
Brock, William A. and Hommes, Cars H. (1997) A rational route to randomness. Econometrica 65, 10591095.CrossRefGoogle Scholar
Chakrabarti, C. G. and Chakraborty, I. (2006) Boltzmann–Shannon entropy: Generalization and application. arXiv: quant-ph/0610177v1.Google Scholar
Chakraborti, Anindya S. and Chakraborti, Bikas K. (2000) Statistical mechanics of money: How saving propensities affects its distribution. European Physical Journal B 17, 167170.CrossRefGoogle Scholar
Clementi, Fabio and Gallegati, Mauro (2005) Pareto’s law of income distribution: Evidence for Germany, the United Kingdom, and the United States. In Chatterjee, Arnab, Yarlagadda, Sudhakar, and Chakrabarti, Bikas K. (eds.), Econophysics of Wealth Distributions, pp. 314. Milan: Springer.CrossRefGoogle Scholar
Cockshott, W. Paul, Cottrell, Allin F., Michaelson, Gregory J., Wright, Ian P., and Yakovenko, Victor M. (2009) Classical Econophysics. Milton Park: Routledge.Google Scholar
Cowell, F. A. and Kugal, K. (1981) Additivity and the entropy concept: An axiomatic approach to inequality measurement. Journal of Economic Theory 25, 131143.CrossRefGoogle Scholar
Cozzolino, J. M. and Zahner, M. J. (1973) The maximum entropy distribution of the future distribution of the future market price of a stock. Operations Research 21, 12001211.CrossRefGoogle Scholar
Davidson, Julius (1919) One of the physical foundations of economics. Quarterly Journal of Economics 33, 717724.CrossRefGoogle Scholar
Dionisio, A., Menezes, R., and Mendes, D. (2009) An econophysics approach to analyze uncertainty in financial markets: An application to the Portuguese stock market. European Physical Journal B 60, 161164.Google Scholar
Dragulescu, Adrian A. and Yakovenko, Victor M. (2009) Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States. Physica A 299, 213221.CrossRefGoogle Scholar
Foley, Duncan K. (1994) A statistical equilibrium theory of markets. Journal of Economic Theory 62, 321345.CrossRefGoogle Scholar
Foley, Duncan K. and Smith, Eric (2008) Classical thermodynamics and economic general equilibrium theory. Journal of Economic Dynamics and Control 32, 765.Google Scholar
Föllmer, Hans (1974) Random economies with many interacting agents. Journal of Mathematical Economics 1, 5162.CrossRefGoogle Scholar
Gallegati, Mauro, Palestrini, Antonio, and Rosser, J. Barkley Jr., (2011) The period of financial distress in speculative markets: Interacting heterogeneous agents and financial constraints. Macroeconomic Dynamics, 15, 6079.CrossRefGoogle Scholar
Georgescu-Roegen, Nicholas (1971) The Entropy Law and the Economic Process. Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Gibbs, Josiah Willard (1902) Elementary Principles of Statistical Mechanics. NewYork: Dover.Google Scholar
Huang, D. W. (2004) Wealth accumulation with random redistribution. Physical Review E 69, 057103.CrossRefGoogle ScholarPubMed
Kindleberger, Charles P. (1978) Manias, Panics, and Crashes. New York: Basic Books.CrossRefGoogle Scholar
Lotka, Alfred J. (1925) Elements of Physical Biology. Baltimore: Williams and Wilkins. Reprinted (1945) as Elements of Mathematical Biology.Google Scholar
Lux, Thomas (2009) Applications of statistical physics in finance and economics. In Rosser, J. Barkley Jr., (ed.) Handbook on Complexity Research, Chapter 9. Cheltenham, UK: Edward Elgar.Google Scholar
Minsky, Hyman P. (1972) Financial instability revisited: The economics of disaster. In Reappraisal of the Federal Reserve Discount Mechanism, vol. 3, pp. 97–136. Washington, DC: Board of Governors.Google Scholar
Montroll, E. W. and Schlesinger, M. F. (1983) Maximum entropy formalism, fractals, scaling phenomena, and 1/f noise: A tale of tails. Journal of Statistical Physics 32, 209230.CrossRefGoogle Scholar
Ostwald, Wilhelm (1908) Die Energie. Leipzig: J.A. Barth.Google Scholar
Pareto, Vilfredo (1897) Cours d’Économie Politique. Lausanne: R. Rouge.Google Scholar
Rényi, Alfréd (1961) On measures of entropy and information. In Neyman, Jerzy (ed.) Proceedings of the Fourth Berkeley Symposium on Mathematics, Statistics, and Probability 1960, Volume 1: Contributions to the Theory of Statistics, pp. 547–561. Berkeley: University of California Press.Google Scholar
Rosser, J. Barkley Jr., (1991) From Catastrophe to Chaos: A General Theory of Economic Discontinuities. Boston: Kluwer.CrossRefGoogle Scholar
Rosser, J. Barkley Jr., (2016) Entropy and econophysics. European Physical Journal – Special Topics 225, 30913104.CrossRefGoogle Scholar
Rosser, J. Barkley Jr., Rosser, Marina V., and Gallegati, Mauro (2012) A Minsky-Kindelberger perspective on the financial crisis. Journal of Economic Issues 45, 449458.CrossRefGoogle Scholar
Samuelson, Paul A. (1947) Foundations of Economic Analysis. Cambridge, MA: Harvard University Press.Google Scholar
Samuelson, Paul A. (1972) Maximum principles in analytical economics. American Economic Review 62, 217.Google Scholar
Samuelson, Paul A. (1990) Gibbs in economics. In Caldi, G. and Mostow, G. D. (eds.) Proceedings of the Gibbs Symposium, pp. 255–267. Providence, RI: American Mathematical Society.Google Scholar
Schinkus, Christoph (2009) Economic uncertainty and econophysics. Physica A 388, 44154423.CrossRefGoogle Scholar
Shaikh, Anwar (2016) Capitalism: Competition, Conflict, and Crises. New York: Oxford University Press.CrossRefGoogle Scholar
Shannon, Claude E. and Weaver, Warren (1949) Mathematical Theory of Communication. Urbana, IL: University of Illinois Press.Google Scholar
Smeeding, Timothy (2012) Income, Wealth, and Debt and the Great Recession. Stanford, CA: Stanford Center on Poverty and Inequality.Google Scholar
Solomon, Sorin and Richmond, Peter (2002) Stable power laws in variable economies: Lotka–Volterra implies Pareto–Zipf. European Physical Journal B 27, 257261.CrossRefGoogle Scholar
Stutzer, Michael J. (1994) The statistical mechanics of asset prices. In Elworthy, K. D., Everitt, W. N., and Lee, E. B. (eds) Differential Equations, Dynamical Systems, and Control Science: A Festschrift in Honor of Lawrence Markus, vol. 152, pp. 321342. New York: Marcel Dekker.Google Scholar
Stutzer, Michael J. (2000) Simple entropic derivation of a generalized Black–Scholes model. Entropy 2, 7077.CrossRefGoogle Scholar
Thurner, S. and Hanel, R. (2012) The entropy of non-ergodic complex systems – A derivation from first principles. International Journal of Modern Physics Conference Series 16, 105115.CrossRefGoogle Scholar
Tsallis, Constantino (1988) Possible generalizations of Boltzmann–Gibbs statistics. Journal of Statistical Physics 52, 479487.CrossRefGoogle Scholar
Uffink, Jos (2014) Boltzmann’s work in statistical physics. In Stanford Encyclopedia of Philosophy. Available at: Scholar
Yakovenko, Victor M., Dragulescu, A. A., Silva, A. C., Banerjee, A., and Di Matteo, T. (2011) Entropy maximization and distribution of money, income, and energy consumption in a market economy. Department of Physics, University of Maryland. Available at: Scholar
Yakovenko, Victor M., and Rosser, J. Barkley Jr., (2009) Colloquium: Statistical mechanics of money, wealth, and income. Reviews of Modern Physics 81, 17041725.CrossRefGoogle Scholar
Zipf, George K. (1941) National Unity and Disunity. Bloomington, IN: Principia Press.Google Scholar
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Available formats

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *