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Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach

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  • Grilli, Luca
  • Santoro, Domenico

Abstract

In this paper we try to build a statistical ensemble to describe a cryptocurrency-based system, emphasizing an "affinity" between the system of agents trading in these currencies and statistical mechanics. We focus our study on the concept of entropy in the sense of Boltzmann and we try to extend such a definition to a model in which the particles are replaced by N agents completely described by their ability to buy and to sell a certain quantity of cryptocurrencies. After providing some numerical examples, we show that entropy can be used as an indicator to forecast the price trend of cryptocurrencies.

Suggested Citation

  • Grilli, Luca & Santoro, Domenico, 2020. "Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach," MPRA Paper 99591, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:99591
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    File URL: https://mpra.ub.uni-muenchen.de/99591/1/MPRA_paper_99591.pdf
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    References listed on IDEAS

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    1. John Y. Campbell & Robert J. Shiller, 1988. "Stock Prices, Earnings and Expected Dividends," Cowles Foundation Discussion Papers 858, Cowles Foundation for Research in Economics, Yale University.
    2. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
    3. McCauley, Joseph l., 2004. "Thermodynamic analogies in economics and finance: instability of markets," MPRA Paper 2159, University Library of Munich, Germany.
    4. Laffont, Jean-Jacques & Ossard, Herve & Vuong, Quang, 1995. "Econometrics of First-Price Auctions," Econometrica, Econometric Society, vol. 63(4), pages 953-980, July.
    5. repec:bla:jfinan:v:43:y:1988:i:3:p:661-76 is not listed on IDEAS
    6. Mihály Ormos & Dávid Zibriczky, 2014. "Entropy-Based Financial Asset Pricing," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-21, December.
    7. A. Dionisio & R. Menezes & D. A. Mendes, 2006. "An econophysics approach to analyse uncertainty in financial markets: an application to the Portuguese stock market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 161-164, March.
    8. Les Gulko, 1999. "The Entropy Theory Of Stock Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 331-355.
    9. Corbet, Shaen & Lucey, Brian & Urquhart, Andrew & Yarovaya, Larisa, 2019. "Cryptocurrencies as a financial asset: A systematic analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 182-199.
    10. Ulrich Kirchner & Caroline Zunckel, 2011. "Measuring Portfolio Diversification," Papers 1102.4722, arXiv.org.
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    Cited by:

    1. Grilli, Luca & Santoro, Domenico, 2020. "Dualism in Bitcoin Dynamics: existence of an Upper Bound in Poincaré Recurrence Theorem for Deterministic vs Stochastic Behavior," MPRA Paper 101057, University Library of Munich, Germany.
    2. Grilli, Luca & Santoro, Domenico, 2020. "How Boltzmann Entropy Improves Prediction with LSTM," MPRA Paper 100578, University Library of Munich, Germany.

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    More about this item

    Keywords

    Cryptocurrency; Entropy; Prices Forecast; Boltzmann; Blockchain;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G19 - Financial Economics - - General Financial Markets - - - Other

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