Statistical mechanics of money

Distinguishable cash, bosonic bitcoin, and fermionic non-fungible token

Kim, Z. Y., & Park, J.-H. (2023) · Frontiers in Physics · doi:10.3389/fphy.2023.1113714 · Cited by 3

H-theorem at negative temperature: the random exchange model with bounds

Lucente, D., Baldovin, M., Andrea Puglisi, B., & Vulpiani, A. (2025) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ada49b · Cited by 3

A mathematical theory for wealth distribution

Düring, B., & Matthes, D. (2010) · Modeling and simulation in science, engineering & technology · doi:10.1007/978-0-8176-4946-3_4 · Cited by 3

Dynamics of three-agent games

Mungan, M., & Rador, T. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/5/055002 · Cited by 3

Job match and income distributions

Li, H., Wang, D., & Chen, X. (2004) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2004.05.030 · Cited by 3

Wealth Distribution Evolution in an Agent-Based Computational Economy

Romanov, V., Yakovlev, D., & Lelchuk, A. (2010) · Lecture notes in economics and mathematical systems · doi:10.1007/978-3-642-13947-5_16 · Cited by 3

On kinetic asset exchange models and beyond: microeconomic formulation,trade network, and all that

Chattejee, A. (2010) · Modeling and simulation in science, engineering & technology · doi:10.1007/978-0-8176-4946-3_2 · Cited by 3

Prospects for Money Transfer Models

Wang, Y., Ding, N., & Xi, N. (2006) · Springer eBooks · doi:10.1007/4-431-28915-1_59 · Cited by 3

CONSERVATIVE SELF-ORGANIZED EXTREMAL MODEL FOR WEALTH DISTRIBUTION

Chakraborty, A., Mukherjee, G., & Manna, S. S. (2012) · Fractals · doi:10.1142/s0218348x12500156 · Cited by 3

Comparative Analysis of Income Distributions in the European Union and the United States

Jagielski, M., Duczmal, R., & Kutner, R. (2015) · Acta Physica Polonica A · doi:10.12693/aphyspola.127.a-75 · Cited by 3

A New Model for Competitive Knowledge Diffusion in Organization Based on the Statistical Thermodynamics

Jong, J.-Y., Wu, W., & So, S.-R. (2020) · Advances in Mathematical Physics · doi:10.1155/2020/8491516 · Cited by 3

The distribution of wealth: an agent-based approach to examine the effect of estate taxation, skill inheritance, and the Carnegie Effect

Kulp, C. W., Kurtz, M. D., Hunt, C., & Velardi, M. (2022) · Journal of Economic Interaction and Coordination · doi:10.1007/s11403-022-00372-7 · Cited by 3

Mean-field optimal control in a multi-agent interaction model for prevention of maritime crime

Orlando, G. (2023) · Advances in Continuous and Discrete Models · doi:10.1186/s13662-023-03771-7 · Cited by 3

Role of Selective Interaction in Wealth Distribution

Gupta, A. K. (2006) · Communications in Computational Physics · doi:10.4208/cicp.2006.v1.p503 · Cited by 3

Global Inequality: How Large is the Effect of Top Incomes?Preprint

Jordá, V., & Niño‐Zarazúa, M. (2017) · SSRN Electronic Journal · doi:10.2139/ssrn.3076788 · Cited by 3

Statistical Mechanics Approach to Econophysics

Yakovenko, V. M. (2022) · Springer eBooks · doi:10.1007/978-3-642-27737-5_169-2 · Cited by 3

Role of Neighbouring Wealth Preference in Kinetic Exchange model of marketPreprint

Banerjee, S. (2023) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.2305.16238 · Cited by 3

A simulation environment for volatility analysis of developed and in development markets

Neto, P. S. G. D. M., Ferreira, T. A. E., & Cavalcanti, G. D. C. (2011) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2011.6033537 · Cited by 2

Co-evolution of network structure and consumer inequality in a spatially explicit model of energetic resource acquisition

Davis, N., Jarvis, A., & Polhill, G. J. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.128261 · Cited by 2

DeTEcT: dynamic and probabilistic parameters extension

Sadykhov, R., Goodell, G., & Treleaven, P. C. (2025) · Frontiers in Blockchain · doi:10.3389/fbloc.2024.1448160 · Cited by 2

A novel Boltzmann probability-based framework for predicting bank credit rating transitions

Viswanathan, H. H. K. K., & Gopinathan, K. N. (2025) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2025.130681 · Cited by 2

Sociophysics of income distributions modeled by deformed fermi-dirac distributions

Dil, E., & Dil, E. (2021) · Journal of Mathematical Sociology · doi:10.1080/0022250x.2021.1973456 · Cited by 2

The Kinetic Theory of Mutation Rates

Pareschi, L., & Toscani, G. (2023) · Axioms · doi:10.3390/axioms12030265 · Cited by 2

Time evolution of the chaos intensity of cryptocurrencies

Alves, P. R. L. (2024) · Nonlinear Dynamics · doi:10.1007/s11071-024-10568-0 · Cited by 2

Statistical Physics Perspective on Economic Inequality

Yakovenko, V. M. (2024) · Routledge eBooks · doi:10.4324/9781003119128-21 · Cited by 2

Hallmarks of deception in asset-exchange models

Blom, K., Makarov, D. E., & Godec, A. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.013279 · Cited by 2

The Rise of Econophysics

Tusset, G. (2026) · Cambridge University Press eBooks · doi:10.1017/9781009439466 · Cited by 2

Some alternative methods for hydrodynamic closures to dissipative kinetic models

Bisi, M., Carrillo, J. A., & SPIGA, G. (2009) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2010-01201-8 · Cited by 2

A multi-agent dynamic model based on different kinds of bequests

Cui, J., Pan, Q., Qian, Q., He, M., & Sun, Q. (2012) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2012.11.021 · Cited by 2

Determinants of Mobility in Random Exchanges

Liu, Q., Wang, Y., & Ding, N. (2008) · International Conference on Wireless Communications, Networking and Mobile Computing · doi:10.1109/wicom.2008.2279 · Cited by 2

Agent-based models of economic interactions

Chakraborti, A., & Germano, G. (2010) · Modeling and simulation in science, engineering & technology · doi:10.1007/978-0-8176-4946-3_1 · Cited by 2

Complex Systems with Trivial Dynamics

López‐Ruiz, R. (2013) · Springer proceedings in complexity · doi:10.1007/978-3-319-00395-5_10 · Cited by 2

Uncertainty of Agricultural product Prices by Information Entropy Model using Probability Distribution for Monthly Prices

Eun, S.-K., Jung, N.-S., Lee, J.-J., & Bae, Y. (2012) · Journal of The Korean Society of Agricultural Engineers · doi:10.5389/ksae.2012.54.2.007 · Cited by 2

The time-dependent characteristics of relative mobility

Huang, J., & Wang, Y. (2013) · Economic Modelling · doi:10.1016/j.econmod.2013.11.019 · Cited by 2

A New Method For Dynamic Stock Clustering Based On Spectral Analysis

Li, Z., & Tian, M. (2016) · Computational Economics · doi:10.1007/s10614-016-9589-9 · Cited by 2

Random exchange models and the distribution of wealth

Scalas, E. (2016) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2016-60162-3 · Cited by 2

Collective Behavior of Equity Returns and Market Volatility

Li, Z., Liu, S., & Tian, M. (2021) · Journal of Data Science · doi:10.6339/jds.201407_12(3).0010 · Cited by 2

An equilibrium-conserving taxation scheme for income from capital

Tempere, J. (2018) · The European Physical Journal B · doi:10.1140/epjb/e2018-80497-x · Cited by 2

Agent-based model of the effect of globalization on inequality and class mobility

Evers, J. H. M., Iron, D., Kolokolnikov, T., & Rumsey, J. (2017) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2017.08.009 · Cited by 2

Fusing non-conservative kinetic market models and evolutionary computing

Luquini, E., Guido Montagna, A., & Omar, N. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.122606 · Cited by 2

Numerical Computations

Trott, M. (2006) · Springer eBooks · doi:10.1007/0-387-28814-7_1 · Cited by 2

The influence of knowledge level on the proportion of wealth in the stock market

Hu, C., & Lai, S. (2022) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2021.0841 · Cited by 2

Optimal income crossover for a two-class model using particle swarm optimization

dos Santos, P. H., Siciliani, I. D. S., & Tragtenberg, M. H. R. (2022) · Physical review. E · doi:10.1103/physreve.106.034313 · Cited by 2

Emergence of Inequality in Income and Wealth Dynamics

Cho, C., Park, J., Mafwele, B. J., Le, Q. A., Park, H. J., & Lee, J. W. (2023) · Entropy · doi:10.3390/e25081129 · Cited by 2

Limits on relief through constrained exchange on random graphs

LaViolette, R. A., Ellebracht, L. A., & Gieseler, C. J. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.04.066 · Cited by 2

Statistical Mechanics Approach to Econophysics

Yakovenko, V. M. (2022) · Encyclopedia of complexity and systems science series · doi:10.1007/978-1-0716-1454-9_169 · Cited by 2

The impact of executive anticipated regret on the choice of incentive system: An econophysics perspective

Ruan, Q., Yang, B., & Ma, G. (2018) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2018.04.002 · Cited by 1

Concentration Effects in a Kinetic Model with Wealth and Knowledge Exchanges

Boudin, L., & Trussardi, L. (2024) · La Matematica · doi:10.1007/s44007-023-00081-y · Cited by 1

Lattice models of random advection and diffusion and their statistics

Stefano Lepri, A., Politi, P., & PIKOVSKY, A. S. (2023) · Physical review. E · doi:10.1103/physreve.108.044150 · Cited by 1

Documenting and Exchanging Simulation Specifications: A Language-Agnostic Approach

Isaac, A. G. (2024) · Social Science Computer Review · doi:10.1177/08944393241246280 · Cited by 1

Extended yard sale model of wealth distribution on Erdős-Rényi random networks

Bibow, N. V. V., & Perotti, J. I. (2025) · Physical review. E · doi:10.1103/8rbw-kr8n · Cited by 1

What the Boltzmann Money Game Teaches Us about Statistical Mechanics (and Maybe Economics)

Makarov, D. E. (2025) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.5c02426 · Cited by 1

Economic Entropy and Sectoral Dynamics: A Thermodynamic Approach to Market Analysis

C., W. A. R., Velandia, A. Z., Wilchez, L. F. Q., & Peña, Y. B. (2026) · Entropy · doi:10.3390/e28070762 · Cited by 1

Exploring the impact of multi-agent wealth exchange model on inequality reduction

Banerjee, S. (2026) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2026.131553 · Cited by 1

Limiting distributions of generalized money exchange models on hypergraphs

Sakagawa, H. (2025) · Advances in Applied Probability · doi:10.1017/apr.2025.10039 · Cited by 1

Energetic Particles from Quasi-separatrix Layers and Current Sheets at the Sun

Schwadron, N. A., Caplan, R. M., Linker, J. A., Palmerio, E., & Young, M. A. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/ae1d6f · Cited by 1

The Fermi–Dirac distribution modeling of income distribution of developing and developed countries: A comparative study of Indonesia, United States, and Singapore

Abhirama, M. A., Dartanto, T., & Purqon, A. (2026) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2026.131287 · Cited by 1

Mixing of the symmetric beta-binomial splitting process on arbitrary graphs

Pymar, R., & Rivera, N. (2026) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/24-aihp1530 · Cited by 1

Towards macroeconomic analysis without microfoundations: measuring the entropy of simulated exchange economies

Luo, Y., MacKay, R. S., & Chater, N. (2026) · Journal of Physics Complexity · doi:10.1088/2632-072x/aea511 · Cited by 1

Relations among different inequality measures in complex systems: From kinetic exchange to earthquake models

Sen, S., Banerjee, S., & Chakrabarti, B. K. (2026) · Physical review. E · doi:10.1103/vnpc-zw1v · Cited by 1

The role of cooperation in spatially explicit economical systems

Lanchier, N., & Reed, S. (2018) · Advances in Applied Probability · doi:10.1017/apr.2018.34 · Cited by 1

Random Market Models with an H-Theorem

López‐Ruiz, R., Shivanian, E., & López, J. L. (2015) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-12328-8_13 · Cited by 1

Evolutionary model of the personal income distribution

Kaldasch, J. (2012) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2012.06.048 · Cited by 1

Income and Wealth Distributions in Money Exchange Models

Xu, Y., Guo, L., & Wang, Y. (2010) · International Conference on E-Business and E-Government · doi:10.1109/icee.2010.1302 · Cited by 1

The wealth exchange model based on agents with different strategies

Sun, Y., Wang, Z., Zhang, L., & He, M. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.10.017 · Cited by 1

Dynamics and kinetic limit for a system of noiseless $d$-dimensional Vicsek-type particles

Gianfelice, M., & Orlandi, E. (2014) · Networks and Heterogeneous Media · doi:10.3934/nhm.2014.9.269 · Cited by 1

A Statistical Physics Analysis of Expenditure in the UK

Oltean, E. (2014) · American Journal of Modern Physics · doi:10.11648/j.ajmp.20140303.13 · Cited by 1

Non-Equilibrium Patterns in the Space of the Stock Market Prices

Gligor, M., & Ignat, M. (2002) · Journal of Non-Equilibrium Thermodynamics · doi:10.1515/jnetdy.2002.022 · Cited by 1

Extremum Criteria for Nonequilibrium States of Dissipative Macroeconomic Systems

Gligor, M. (2005) · Elsevier eBooks · doi:10.1016/b978-008044488-8/50037-0 · Cited by 1

Network Theory in Macroeconomics and Finance

Chakrabarti, A. S. (2017) · New economic windows · doi:10.1007/978-3-319-47705-3_5 · Cited by 1

Income and Wealth Distributions from Stochastic Strategy Minority Game

Ghosh, A., & Biswas, S. (2017) · Reports in Advances of Physical Sciences · doi:10.1142/s2424942417400035 · Cited by 1

A Fundamental Concept of Inequality in the Perspective of Paretian Economics

Maialeh, R. (2016) · Politická ekonomie · doi:10.18267/j.polek.1121 · Cited by 1

A Stochastic Trading Model of Wealth Distribution

Yarlagadda, S., & Das, A. (2005) · New economic windows · doi:10.1007/88-470-0389-x_14 · Cited by 1

An Econophysical Dynamic Approach of Expenditure and Income Distribution in the UK

Oltean, E. (2014) · American Journal of Physics and Applications · doi:10.11648/j.ajpa.20140203.11 · Cited by 1

Methods of kinetic theory in problems of econophysics

Aristov, V. V. (2019) · AIP conference proceedings · doi:10.1063/1.5119676 · Cited by 1

Structure of the IBEX Ribbon from Distributed Sources

Schwadron, N. A., & McComas, D. J. (2019) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1332/1/012013 · Cited by 1

The Dynamic Model of Market Inequality

Maialeh, R. (2020) · Contributions to economics · doi:10.1007/978-3-030-46313-7_7 · Cited by 1

Effect of Savings on a Gas-Like Model Economy with Credit and Debt

Chacón‐Acosta, G., & Ángeles-Sánchez, V. (2021) · Entropy · doi:10.3390/e23020196 · Cited by 1

Complex system properties in the spreading of COVID-19 pandemic

Quimbay, C. J. (2021) · Revista de la Academia Colombiana de Ciencias Exactas Físicas y Naturales · doi:10.18257/raccefyn.1459 · Cited by 1

Information‐theoretic model of induced technical change: Theory and empirics

Yang, J. (2022) · Metroeconomica · doi:10.1111/meca.12399 · Cited by 1

Per capita wealth in cities and regions fitted to Pareto, stretched exponential and econophysics Boltzmann–Gibbs distributions

Sánchez-Espinosa, D. B., Hernández-Casildo, J., Hernández-Ramírez, E., & del Castillo‐Mussot, M. (2022) · International Journal of Modern Physics C · doi:10.1142/s0129183123500171 · Cited by 1

Agent-Based Models

Atenas, B., Larroza, E., & Bahoz, V. (2024) · IntechOpen eBooks · doi:10.5772/intechopen.1008198 · Cited by 1

Condensation Phenomena and Pareto Distribution in Disordered Urn Models

Inoue, J., & Ohkubo, J. (2010) · New economic windows · doi:10.1007/978-88-470-1501-2_7 · Cited by 1

Stability of the Distribution in a Money Exchange Model

Chun-Bin, Y. (2004) · Chinese Physics Letters · doi:10.1088/0256-307x/21/1/064 · Cited by 1

Period Analysis of Multiplier in Agent-Based Models

Xu, Y., Wang, Y., & Ding, N. (2008) · International Conference on Wireless Communications, Networking and Mobile Computing · doi:10.1109/wicom.2008.2605 · Cited by 1

4 DYNAMICS AND KINETIC LIMIT FOR A SYSTEM OF NOISELESS d-DIMENSIONAL VICSEK-TYPE PARTICLESPreprint

Gianfelice, M., & Orlandi, E. (2016) · Cited by 1

Dependence of Distribution and Velocity of Money on Required Reserve Ratio

Xi, N., Ding, N., & Wang, Y. (2006) · Springer eBooks · doi:10.1007/4-431-28915-1_58 · Cited by 1

Money Distributions in Chaotic EconomiesPreprint

Pellicer-Lostao, C., & López‐Ruiz, R. (2009) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.0906.1899

Introducing Chaos in Economic Gas-like ModelsPreprint

Pellicer-Lostao, C., & López‐Ruiz, R. (2009) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.0904.0344

Statistical physics for compressed sensing and information hiding

Manoel, A. A. M. (2015) · Digital Library of Theses and Dissertations (Universidade de São Paulo) · doi:10.11606/t.43.2015.tde-08102015-140952

Statistical Thermodynamics Concepts and Mathematical Tools for a Multi-Agent Ecosystem

Segovia, J. (2014) · Artificial Life · doi:10.1162/artl_a_00128

Broad distributions from resource partitioning

Malescio, G. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.05.016

THE WEALTH DISTRIBUTION MODEL WITH THE KICKBACK RATE

ZHANG, Y., & He, M. (2008) · International Journal of Modern Physics C · doi:10.1142/s0129183108013096

The trading rectangle strategy within book models

Matassini, L. (2001) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(01)00405-8

In Search of H-theorem for Ulam’s Redistribution of Energy Problem

Apenko, S. M. (2015) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-12328-8_12

Dynamic equity theory : modeling pay for performance's cross-level effect

Phang, R. (2015) · DR-NTU (Nanyang Technological University) · doi:10.32657/10356/65643

Local operators in kinetic wealth distribution

Andrecut, M. (2016) · International Journal of Modern Physics C · doi:10.1142/s0129183116501321

Learning What to Want: Data-Driven MicrofoundationsPreprint

Srivastava, N., & Schrater, P. (2014) · SSRN Electronic Journal · doi:10.2139/ssrn.2526540

Statistical Physics Models for Group Decision Making

Gligor, M. (2013) · Elsevier eBooks · doi:10.1016/b978-0-12-404626-9.00009-8

Economic Inequality as a Statistical Outcome

Kafri, O., & Fishof, E. (2016) · Journal of Economics Bibliography · doi:10.1453/jeb.v3i4.1004

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