IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v414y2014icp108-117.html
   My bibliography  Save this article

Clausius inequality and H-theorems for some models of random wealth exchange

Author

Listed:
  • Apenko, Sergey M.

Abstract

We discuss a possibility of deriving an H-theorem for nonlinear discrete time evolution equation that describes random wealth exchanges. In such kinetic models economical agents exchange wealth in pairwise collisions just as particles in a gas exchange their energy. It appears useful to reformulate the problem and represent the dynamics as a combination of two processes. The first is a linear transformation of a two-particle distribution function during the act of exchange while the second one corresponds to new random pairing of agents and plays a role of some kind of feedback control. This representation leads to a Clausius-type inequality which suggests a new interpretation of the exchange process as an irreversible relaxation due to a contact with a reservoir of a special type. Only in some special cases when equilibrium distribution is exactly a gamma distribution, this inequality results in the H-theorem with monotonically growing ‘entropy’ functional which differs from the Boltzmann entropy by an additional term. But for arbitrary exchange rule the evolution has some features of relaxation to a non-equilibrium steady state and it is still unclear if any general H-theorem could exist.

Suggested Citation

  • Apenko, Sergey M., 2014. "Clausius inequality and H-theorems for some models of random wealth exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 108-117.
    • Handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:108-117
    DOI: 10.1016/j.physa.2014.07.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711400586X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.07.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chakrabarti,Bikas K. & Chakraborti,Anirban & Chakravarty,Satya R. & Chatterjee,Arnab, 2013. "Econophysics of Income and Wealth Distributions," Cambridge Books, Cambridge University Press, number 9781107013445, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kiran Sharma & Subhradeep Das & Anirban Chakraborti, 2017. "Global Income Inequality and Savings: A Data Science Perspective," Papers 1801.00253, arXiv.org, revised Aug 2018.
    2. Hutzler, S. & Sommer, C. & Richmond, P., 2016. "On the relationship between income, fertility rates and the state of democracy in society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 9-18.
    3. Venkatasubramanian, Venkat & Luo, Yu & Sethuraman, Jay, 2015. "How much inequality in income is fair? A microeconomic game theoretic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 120-138.
    4. Maia, Adriano & Matsushita, Raul & Demarcus, Antonio & Da Silva, Sergio, 2023. "Scalability in a two-class interoccupational earnings distribution model," SocArXiv 23brg, Center for Open Science.
    5. Ion Santra, 2022. "Effect of tax dynamics on linearly growing processes under stochastic resetting: a possible economic model," Papers 2202.13713, arXiv.org.
    6. Smerlak, Matteo, 2016. "Thermodynamics of inequalities: From precariousness to economic stratification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 40-50.
    7. Eliazar, Iddo, 2017. "Inequality spectra," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 824-847.
    8. Ghosh, Asim & Chakrabarti, Bikas K., 2021. "Limiting value of the Kolkata index for social inequality and a possible social constant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    9. Jacques Tempere, 2018. "An equilibrium-conserving taxation scheme for income from capital," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(2), pages 1-6, February.
    10. Aur'elien Hazan, 2017. "Stock-flow consistent macroeconomic model with nonuniform distributional constraint," Papers 1708.00645, arXiv.org.
    11. Kayser, Kirk & Armbruster, Dieter, 2019. "Social optima of need-based transfers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    12. Istvan Gere & Szabolcs Kelemen & Geza Toth & Tamas Biro & Zoltan Neda, 2021. "Wealth distribution in modern societies: collected data and a master equation approach," Papers 2104.04134, arXiv.org.
    13. Yong Tao & Xiangjun Wu & Tao Zhou & Weibo Yan & Yanyuxiang Huang & Han Yu & Benedict Mondal & Victor M. Yakovenko, 2019. "Exponential structure of income inequality: evidence from 67 countries," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(2), pages 345-376, June.
    14. Kiran Sharma & Parul Khurana, 2021. "Growth and dynamics of Econophysics: a bibliometric and network analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(5), pages 4417-4436, May.
    15. Eliazar, Iddo, 2015. "The sociogeometry of inequality: Part II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 116-137.
    16. Mukherjee, Sudip & Biswas, Soumyajyoti & Chatterjee, Arnab & Chakrabarti, Bikas K., 2021. "The Ising universality class of kinetic exchange models of opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    17. Anirban Chakraborti & Damien Challet & Arnab Chatterjee & Matteo Marsili & Yi-Cheng Zhang & Bikas K. Chakrabarti, 2013. "Statistical Mechanics of Competitive Resource Allocation using Agent-based Models," Papers 1305.2121, arXiv.org, revised Sep 2014.
    18. Sergey Rashkovskiy, 2020. "Thermodynamics of markets," Papers 2010.10260, arXiv.org.
    19. Costas J. Efthimiou & Adam Wearne, 2016. "Household income distribution in the USA," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(3), pages 1-6, March.
    20. D. S. Quevedo & C. J. Quimbay, 2019. "Piketty's second fundamental law of capitalism as an emergent property in a kinetic wealth-exchange model of economic growth," Papers 1903.00952, arXiv.org, revised Mar 2019.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:108-117. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.