Statistical mechanics of money

Economic thermodynamics

Rashkovskiy, S. A. (2021) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2021.126261 · Cited by 14

Uncovering a Two-Phase Dynamics from a Dollar Exchange Model with Bank and Debt

Cao, F., & Motsch, S. (2023) · SIAM Journal on Applied Mathematics · doi:10.1137/22m1518621 · Cited by 14

Social inequality: from data to statistical physics modeling

Chatterjee, A., Ghosh, A., Inoue, J.-I., & Chakrabarti, B. K. (2015) · Journal of Physics Conference Series · doi:10.1088/1742-6596/638/1/012014 · Cited by 14

Properties of wealth distribution in multi-agent systems of a complex network

Hu, M.-B., Jiang, R., Wu, Y., Wang, R., & Wu, Q. (2008) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2008.06.032 · Cited by 14

Wealth redistribution in conservative linear kinetic models

Toscani, G. (2009) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/88/10007 · Cited by 14

The Rich Are Different ! Pareto Law from Asymmetric Interactions in Asset Exchange Models

Sitabhra Sinha, A. (2005) · New economic windows · doi:10.1007/88-470-0389-x_18 · Cited by 14

POWER-LAW DISTRIBUTIONS IN CIRCULATING MONEY: EFFECT OF PREFERENTIAL BEHAVIOR

Ding, N., Wang, Y., XU, J., & Xi, N. (2004) · International Journal of Modern Physics B · doi:10.1142/s0217979204025981 · Cited by 14

Thermodynamics of markets

Rashkovskiy, S. A. (2020) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2020.125699 · Cited by 13

Statistical Physics of Economic Systems: a Survey for Open Economies

Tao, Y., & Chen, X. (2012) · Chinese Physics Letters · doi:10.1088/0256-307x/29/5/058901 · Cited by 13

The Role of Temperature in Economic Exchange - An Empirical Analysis

Dimitrijević, B., & Lovre, I. (2015) · Journal of Central Banking Theory and Practice · doi:10.1515/jcbtp-2015-0012 · Cited by 13

A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory

Bargigli, L., Viaggiu, S., & Lionetto, A. (2016) · Journal of Statistical Physics · doi:10.1007/s10955-016-1599-4 · Cited by 13

Modelling Inequality

Thébault, K. P. Y., Bradley, S., & Reutlinger, A. (2018) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/axw028 · Cited by 13

Nonlinear redistribution of wealth from a stochastic approach

Lima, H., Vieira, A. R., & Anteneodo, C. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.112578 · Cited by 13

Statistical Thermodynamics of Economic Systems

Quevedo, H., & Quevedo, M. N. (2011) · Journal of Thermodynamics · doi:10.1155/2011/676495 · Cited by 13

LGEM: A lattice Boltzmann economic model for income distribution and tax regulation

Boluda, J. C., Montoliu, C., & Colom, R. J. (2011) · Mathematical and Computer Modelling · doi:10.1016/j.mcm.2011.10.051 · Cited by 13

Herd Behavior and Financial Crashes: An Interacting Particle System Approach

Crescimanna, V., & Persio, L. D. (2016) · Journal of Mathematics · doi:10.1155/2016/7510567 · Cited by 13

Transition from Pareto to Boltzmann–Gibbs behavior in a deterministic economic model

González-Estévez, J., Cosenza, M. G., Alvarez-Llamoza, O., & López‐Ruiz, R. (2009) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2009.04.031 · Cited by 13

A kinetic description of mutation processes in bacteria

Toscani, G. (2013) · Kinetic and Related Models · doi:10.3934/krm.2013.6.1043 · Cited by 13

The distribution of wealth in the presence of altruism in simple economic models

Rodríguez-Achach, M., & Huerta-Quintanilla, R. (2005) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.07.001 · Cited by 13

Quantum games entropy

Hidalgo, E. G. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.05.001 · Cited by 13

Emergence of power-law in a market with mixed models

Saif, M. A., & Gade, P. M. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.03.058 · Cited by 13

Emergence of income inequality: Origin, distribution and possible policies

Tian, S., & Liu, Z. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.122767 · Cited by 12

Statistical Description of Human Addiction Phenomena

Toscani, G. (2021) · SEMA SIMAI Springer series · doi:10.1007/978-3-030-67104-4_7 · Cited by 12

World per capita gross domestic product measured nominally and across countries with purchasing power parity: Stretched exponential or Boltzmann–Gibbs distribution?

Hernández-Ramírez, E., del Castillo‐Mussot, M., & Hernández-Casildo, J. (2020) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2020.125690 · Cited by 12

Uniform propagation of chaos for a dollar exchange econophysics model

Cao, F., & Cortez, R. (2024) · European Journal of Applied Mathematics · doi:10.1017/s0956792524000184 · Cited by 12

Mixing it up

Schneider, M., & Scharfenaker, E. (2020) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2020-900130-4 · Cited by 12

The shape of educational inequality

Quarles, C. L., Budak, C., & Resnick, P. (2020) · Science Advances · doi:10.1126/sciadv.aaz5954 · Cited by 12

From the binomial reshuffling model to Poisson distribution of money

Cao, F., & Marshall, N. F. (2024) · Networks and Heterogeneous Media · doi:10.3934/nhm.2024002 · Cited by 12

Redistribution Spurs Growth by Using a Portfolio Effect on Risky Human Capital

Lorenz, J., Paetzel, F., & Schweitzer, F. (2013) · PLoS ONE · doi:10.1371/journal.pone.0054904 · Cited by 12

Labor Market Segmentation and Immigrant Competition: A Quantal Response Statistical Equilibrium Analysis

Wiener, N. M. (2020) · Entropy · doi:10.3390/e22070742 · Cited by 12

Living in an irrational society: Wealth distribution with correlations between risk and expected profits

Fuentes, M., Kuperman, M. N., & Iglesias, J. R. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2006.04.088 · Cited by 12

Congestion and Cascades in Payment SystemsPreprint

Beyeler, W., Glass, R. J., Bech, M. L., & Soramäki, K. (2006) · SSRN Electronic Journal · doi:10.2139/ssrn.932594 · Cited by 12

Thermodynamic Analysis of Financial Markets: Measuring Order Book Dynamics with Temperature and Entropy

Li, H., Xiao, Y., Polukarov, M., & Ventre, C. (2023) · Entropy · doi:10.3390/e26010024 · Cited by 11

Information of Complex Systems and Applications in Agent Based Modeling

Bao, L., & Fritchman, J. C. (2018) · Scientific Reports · doi:10.1038/s41598-018-24570-1 · Cited by 11

Common origin of power-law tails in income distributions and relativistic gases

Modanese, G. (2015) · Physics Letters A · doi:10.1016/j.physleta.2015.09.004 · Cited by 11

Age-related changes in the distributions of depressive symptom items in the general population: a cross-sectional study using the exponential distribution model

Tomitaka, S., Kawasaki, Y., Ide, K., Yamada, H., Furukawa, T. A., & Ono, Y. (2016) · PeerJ · doi:10.7717/peerj.1547 · Cited by 11

A Stylised Model for Wealth Distribution

Düring, B., Georgiou, N., & Scalas, E. (2017) · Evolutionary economics and social complexity science · doi:10.1007/978-981-10-5705-2_7 · Cited by 11

Development of Econophysics: A Biased Account and Perspective from Kolkata

Chakrabarti, B. K., & Sinha, A. (2021) · Entropy · doi:10.3390/e23020254 · Cited by 11

Inferring the drivers of language change using spatial models

Burridge, J., & Blaxter, T. (2021) · Journal of Physics Complexity · doi:10.1088/2632-072x/abfa82 · Cited by 11

Functional niche constraints on carnivore assemblages (Mammalia: Carnivora) in the Americas: What facilitates coexistence through space and time?

Arias‐Alzate, A., Arroyave, F. J., Romero‐Goyeneche, O. Y., Hurtado-Heredia, R., González-Maya, J. F., Arroyo‐Cabrales, J., Peterson, A. T., & Martínez‐Meyer, E. (2022) · Journal of Biogeography · doi:10.1111/jbi.14319 · Cited by 11

La simulation à base d’agents en sciences sociales : une « béquille pour l’esprit humain1 »?

Banos, A. (2010) · Nouvelles perspectives en sciences sociales · doi:10.7202/044078ar · Cited by 11

Boltzmann–Gibbs distribution of fortune and broken time reversible symmetry in econodynamics

Ao, P. (2005) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2005.07.004 · Cited by 11

Econophysics: finance, economics and physics

Ray, R. (2010) · Applied Economics Letters · doi:10.1080/13504851003596020 · Cited by 11

Hysteresis of economic networks in an XY model

Hosseiny, A., Absalan, M., Sherafati, M., & Gallegati, M. (2018) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2018.08.064 · Cited by 11

Enthalpy of Combustion on n ‐Alkanes. Quantum Chemical Calculations up to n ‐C 60 H 122 and Power Law Distributions

Audran, G., Marque, S. R. A., Siri, D., & Santelli, M. (2018) · ChemistrySelect · doi:10.1002/slct.201802021 · Cited by 11

Nonequilibrium thermodynamics of wealth condensation

Braun, D. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2006.01.085 · Cited by 11

Wealth Thermalization Hypothesis and Social Networks

Frahm, K. M., & Shepelyansky, D. L. (2026) · Journal of Statistical Physics · doi:10.1007/s10955-026-03621-2 · Cited by 10

Equilibrium distributions and relaxation times in gaslike economic models: An analytical derivation

Calbet, X., López, J. L., & López‐Ruiz, R. (2011) · Physical Review E · doi:10.1103/physreve.83.036108 · Cited by 10

On the efficient resources distribution in economics based on entropy

Antoniou, I. E., Иванов, В. В., Kryanev, A. V., Matokhin, V. V., & Shapovalov, M. V. (2004) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2003.12.051 · Cited by 10

Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties

Medaglia, A., Tosin, A., & Zanella, M. (2022) · Partial Differential Equations and Applications · doi:10.1007/s42985-022-00189-w · Cited by 10

Complex systems perspective in assessing risks in artificial intelligence

Kondor, D., Hafez, V., Shankar, S., Wazir, R., & Karimi, F. (2024) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2024.0109 · Cited by 10

Thermodynamics of firms' growth

Zambrano, E., Hernando, A., Bariviera, A. F., Hernando, R., & Plastino, A. (2015) · Journal of The Royal Society Interface · doi:10.1098/rsif.2015.0789 · Cited by 10

Inequality reversal: Effects of the savings propensity and correlated returns

Chakrabarti, A. S., & Chakrabarti, B. K. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2010.04.038 · Cited by 10

A combined model of aggregation, fragmentation, and exchange processes: insights from analytical calculations

Robson, D. T., Baas, A. C. W., & Annibale, A. (2021) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/abfa1d · Cited by 10

Preliminary Comparison of Households' Income in Poland with European Union and United States Ones by Using the Statistical Physics Methods

Jagielski, M., Kutner, R., & Pęczkowski, M. (2012) · Acta Physica Polonica A · doi:10.12693/aphyspola.121.b-47 · Cited by 10

Mathematics and physics applications in sociodynamics simulation: the case of opinion formation and diffusion

Aletti, G., Naimzada, A. K., & Naldi, G. (2010) · Modeling and simulation in science, engineering & technology · doi:10.1007/978-0-8176-4946-3_8 · Cited by 10

Multiplicative asset exchange with arbitrary return distributions

Moukarzel, C. F. (2011) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2011/08/p08023 · Cited by 10

Breakdown of the mean-field approximation in a wealth distribution model

Medo, M. (2009) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2009/02/p02014 · Cited by 10

Effect of segregation on inequality in kinetic models of wealth exchange

Fernandes, L., & Tempere, J. (2020) · The European Physical Journal B · doi:10.1140/epjb/e2020-100534-7 · Cited by 10

A simple and efficient kinetic model for wealth distribution with saving propensity effect: Based on lattice gas automaton

Cui, L., & Lin, C. (2020) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2020.125283 · Cited by 10

Economic Arbitrage and the Econophysics of Income Inequality

Shaikh, A. M., & Jacobo, J. E. (2020) · Review of Behavioral Economics · doi:10.1561/105.00000129 · Cited by 10

Derivation of the Maxwellian distribution from the microcanonical ensemble

López‐Ruiz, R., & Calbet, X. (2007) · American Journal of Physics · doi:10.1119/1.2737472 · Cited by 10

Non-life insurance pricing: multi-agent model

Darooneh, A. H. (2004) · The European Physical Journal B · doi:10.1140/epjb/e2004-00363-x · Cited by 10

Capital death in the world market

Avakian, A., Boris Podobnik, A., Piskor, M., & Stanley, E. (2014) · Physical Review E · doi:10.1103/physreve.89.032805 · Cited by 9

Geometrothermodynamic approach in econophysics

Quevedo, H., & Quevedo, M. N. (2022) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887823500573 · Cited by 9

An analogy of the size distribution of business firms with Bose–Einstein statistics

Hernandez-Perez, R. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2010.05.024 · Cited by 9

Keynesian multiplier versus velocity of money

Wang, Y., Xu, Y., & Liu, L. (2010) · Physics Procedia · doi:10.1016/j.phpro.2010.07.009 · Cited by 9

What’s Wrong with Today’s Economics?The CurrentCrisis Calls for an Approach to Economics Rooted Moreon Data Than on Rationality

Focardi, S. M., & Fabozzi, F. J. (2012) · The Journal of Portfolio Management · doi:10.3905/jpm.2012.38.3.104 · Cited by 9

Income and poverty in a developing economy

Chattopadhyay, A. K., Ackland, G. J., & Mallick, S. (2010) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/91/58003 · Cited by 9

Influence of Money Distribution on Civil Violence Model

Ormazábal, I., Borotto, F. A., & Astudillo, H. F. (2017) · Complexity · doi:10.1155/2017/7453560 · Cited by 9

Coupled Criticality Analysis of Inflation and Unemployment

Lai, Z. K., Namaki, A., Hosseiny, A., Jafari, G., & Ausloos, M. (2020) · Entropy · doi:10.3390/e23010042 · Cited by 9

Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies

Griffin, C. H., Rajtmajer, S. M., Squicciarini, A., & Belmonte, A. L. (2019) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/16m109675x · Cited by 9

Comments on “Worrying Trends in Econophysics”: Income Distribution Models

Richmond, P., Chakrabarti, B. K., Chatterjee, A., & Angle, J. (2007) · Springer eBooks · doi:10.1007/978-88-470-0502-0_27 · Cited by 9

Kinetic models for systems of interacting agents with multiple microscopic states

Bisi, M., & Loy, N. (2023) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2023.133967 · Cited by 8

Growth and allocation of resources in economics: The agent-based approach

Scalas, E., Gallegati, M., Guerci, É., Mas, D., & Tedeschi, A. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2006.04.038 · Cited by 8

Assessing geographical effects in spatial diffusion processes: The case of euro coins

Texier, M. L., & Caruso, G. (2016) · Computers Environment and Urban Systems · doi:10.1016/j.compenvurbsys.2016.08.003 · Cited by 8

Kinetic Models of Wealth Distribution with Extreme Inequality: Numerical Study of Their Stability against Random Exchanges

Ghosh, A. K., Banerjee, S., Goswami, S., Mitra, M., & Chakrabarti, B. K. (2023) · Entropy · doi:10.3390/e25071105 · Cited by 8

Income distribution: Boltzmann analysis and its extension

Yuqing, H. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2006.11.009 · Cited by 8

Money creation process in a random redistribution model

Chen, S., Wang, Y., Li, K., & Wu, J. (2013) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2013.09.036 · Cited by 8

Agent based models for wealth distribution with preference in interaction

Goswami, S., & Sen, P. (2014) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2014.08.018 · Cited by 8

The Nonuniversality of Wealth Distribution Tails Near Wealth Condensation Criticality

Polk, S. L., & Boghosian, B. M. (2021) · SIAM Journal on Applied Mathematics · doi:10.1137/19m1306051 · Cited by 8

Patterns of item score and total score distributions on depression rating scales in the general population: evidence and mechanisms

Tomitaka, S. (2020) · Heliyon · doi:10.1016/j.heliyon.2020.e05862 · Cited by 8

The economic mobility in money transfer models

Ding, N., Xi, N., & Wang, Y. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.11.043 · Cited by 8

Mathematical Models for Socio-economic Problems

Bertotti, M. L., & Modanese, G. (2014) · Springer INdAM series · doi:10.1007/978-3-319-02657-2_10 · Cited by 8

Econophysics of Wealth Distribution: A Comment

Anglin, P. M. (2005) · New economic windows · doi:10.1007/88-470-0389-x_27 · Cited by 8

Kinetic and mean field description of Gibrat’s law

Toscani, G. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.06.063 · Cited by 8

Econophysics: making sense of a chimera

Yee, A. K. (2021) · European Journal for Philosophy of Science · doi:10.1007/s13194-021-00413-1 · Cited by 8

NONLIFE INSURANCE PRICING: STATISTICAL MECHANICS VIEWPOINT

Darooneh, A. H. (2005) · International Journal of Modern Physics C · doi:10.1142/s0129183105007005 · Cited by 8

Dynamics of multi-player games

Ben-Naim, E., Kahng, B., & Kim, J. S. (2006) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2006/07/p07001 · Cited by 8

Decentralized token economy theory (DeTEcT): token pricing, stability and governance for token economies

Sadykhov, R., Goodell, G., De Montigny, D., Schoernig, M., & Treleaven, P. (2023) · Frontiers in Blockchain · doi:10.3389/fbloc.2023.1298330 · Cited by 7

New multi-parametric analytical approximations of exponential distribution with power law tails for new cars sells and other applications

Garanina, O. S., & Romanovsky, M. Y. (2015) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2015.01.068 · Cited by 7

TRANSITION FROM EXPONENTIAL TO POWER LAW INCOME DISTRIBUTIONS IN A CHAOTIC MARKET

Pellicer-Lostao, C., & LOPEZ-RUIZ, R. (2011) · International Journal of Modern Physics C · doi:10.1142/s0129183111016038 · Cited by 7

Some universal patterns in income distribution: An econophysics approach

Shaikh, A. M., & Ragab, A. (2022) · Metroeconomica · doi:10.1111/meca.12412 · Cited by 7

Distribution of Money on Connected Graphs with Multiple Banks

Lanchier, N., & Reed, S. (2024) · Mathematical Modelling of Natural Phenomena · doi:10.1051/mmnp/2024009 · Cited by 7

A biased dollar exchange model involving bank and debt with discontinuous equilibrium

Cao, F., & Reed, S. (2025) · Mathematical Modelling of Natural Phenomena · doi:10.1051/mmnp/2025007 · Cited by 7

Statistical ensembles for money and debt

Viaggiu, S., Lionetto, A., Bargigli, L., & Longo, M. (2012) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2012.05.027 · Cited by 7

Income distribution in the European Union versus in the United States

Jagielski, M., Duczmal, R., & Kutner, R. (2015) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2015.03.071 · Cited by 7

Directed Random Market: The Equilibrium Distribution

Katriel, G. (2014) · Acta Applicandae Mathematicae · doi:10.1007/s10440-014-9971-3 · Cited by 7

An Econophysical Approach of Polynomial Distribution Applied to Income and Expenditure

Oltean, E. (2014) · American Journal of Modern Physics · doi:10.11648/j.ajmp.20140302.18 · Cited by 7

The velocity of money in a life-cycle model

Wang, Y., & Qiu, H. (2005) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.01.053 · Cited by 7

XXXI Encontro Nacional de F́ısica da Matéria Condensada / ID: 862-1 1 Statistical Mechanics of Money in a Closed Economic System

Gomes, R. A., & Leão, S. D. A. (2014)

Statistical mechanics approach to the probability distribution of moneyPreprint

Yakovenko, V. M. (2010) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1007.5074 · Cited by 17

Nonequilibrium statistical mechanics of money/energy exchange models

Miao, M., Makarov, D. E., & Blom, K. (2024) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad369b · Cited by 4

ContentsPreprint

Yakovenko, V. M., & Rosser, J. B. (2009)

Colloquium : Statistical mechanics of money, wealth, and income

Yakovenko, V. M., & Rosser, J. B. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.1703 · Cited by 559