Grilli, Luca and Santoro, Domenico (2020): Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach.

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Abstract
In this paper we try to build a statistical ensemble to describe a cryptocurrencybased 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.
Item Type:  MPRA Paper 

Original Title:  Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach 
English Title:  Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach 
Language:  English 
Keywords:  Cryptocurrency, Entropy, Prices Forecast, Boltzmann, Blockchain 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69  Other E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates > E44  Financial Markets and the Macroeconomy E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates > E47  Forecasting and Simulation: Models and Applications G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates G  Financial Economics > G1  General Financial Markets > G17  Financial Forecasting and Simulation G  Financial Economics > G1  General Financial Markets > G19  Other 
Item ID:  99591 
Depositing User:  Dr. Domenico Santoro 
Date Deposited:  17 Apr 2020 10:47 
Last Modified:  17 Apr 2020 10:47 
References:  Antonopoulos A. A. Mastering Bitcoin: Unlocking Digital Cryptocurrencies. O’Reilly Media, 2014. Dionisio A., Menezes R, and Menezes D. A. An econophysics approach to analyse uncertainty in financial markets: an application to the portuguese stock market. The European Physical Journal, 2006. Krennikov A. The financial heat machine: coupling with the present financial crises. Wilmott, 2012. Rényi A. Probability theory. NorthHolland Series in Applied Mathematics and Mechanics, 1970. Brissaud J. B. The meanings of entropy. Entropy, 2005. BaFin. Merkblatt: Hinweise zum tatbenstand des kryptoverwahrgeschafts. 2020. Philippatos G. C. and Wilson C. J. Entropy, market risk and the selection of efficient portfolios. Applied Economics, 1972. Tsallis C. Possible generalization of boltzmanngibbs statistics. SpringerVerlag, 1988. Shannon C. E. and Weaver W. The mathematical theory of communication. University of Illinois Press, 1949. Smith E. and Foley D. K. Is utility theory so different from thermodynamics? SFI Preprint, 2002. Fama E. F. and French K. R. Dividend yields and expected stock returns. Journal of Financial Economics, 1988. Perasan M. H. and Timmermann A. Predictability of stock returns: Robustness and economic significance. The Journal of Finance, 1995. Usta I. and Kantar Y. M. Meanvarianceskewnessentropy measures: a multi objective approach for portfolio selection. Entropy, 2011. IFRS. Holdings of cryptocurrencies  agenda paper 12. IFRS Staff Paper, 2019. Chen J., Duan K., Zhang R., Zeng L., and Wang W. An ai based super nodes selection algorithm in blockchain networks. arXiv:1808.00216, 2018. McCauley J. Thermodynamic analogies in economics and finance: instability of markets. MPRA, 2004. Laffont J.J., Ossard H., and Vuong Q. Econometrics of firstprice auctions. Econometrica, 1995. Huang K. Statistical Mechanics. Wiley, 2008. Adler R. L., Konheim A. G., and McAndrew M. H. Topological entropy. American Mathematical Society, 1965. Boltzmann L. Vorlesungen uber gastheorie. Leipzig: J. A. Barth., 1896. Gulko L. The entropy theory of stock option pricing. Int. J. Theoretical Appl. Finance, 1999. Falcioni M. and Vulpiani A. Meccanica Statistica Elementare. SpringerVerlag, 2015. Ormos M. and Zibriczky D. Entropybased financial asset pricing. PLoS ONE 9(12):e115742, 2014. Pincus S. M. Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Science, 1991. Qi M. and Maddala G. S. Economic factors and the stock market: a new perspective. Wiley, 1999. Sergeev V. M. Rationality, property rights, and thermodynamic approach to market equilibrium. Journal of Mathematical Sciences, 2006. Sheraz M., Dedu S., and Preda V. Entropy measures for assering volatile markets. Procedia Economics and Finance, 2014. Szmigiera M. Number of blockchain wallet users globally 20162019. Statista, 2020. Nawrocki D. N. and Harding W. H. Statevalue weighted entropy as a measure of investment risk. Applied Economics, 1985. Jana P., Roy T. K., and Mazumder S. K. Multiobjective possibilistic model for portfolio selection with transaction cost. J. Comput. Appl. Math., 2009. Clausius R. Ueber verschiedene fur die anwendung bequeme formen der hauptgleichungen der mechanischen warmetheorie. Ann. Phys. Chem., 1865. Corbet S., Lucey B., Urquhart A., and Yarovaya L. Cryptocurrencies as a financial asset: A systematic analysis. Elsevier, 2019. Nakamoto S. Bitcoin: A pertopeer electronic cash system. Bitcoin.org, 2008. Viaggiu S., Lionetto A., Bargigli L., and Longo M. Statistical ensembles for money and debt. arXiv:1109.0891, 2018. Kirchner U. and Zunchel C. Measuring portfolio diversification. arXiv:1102.4722, 2011. Zakiras V., Christopoulos A. G., and Rendoumis V. L. A thermodynamic description of the time evolution of a stock market index. European Journal of Economics, Finance and Administrative Sciences, 2009. Chen W., Wang Z., Xie H., and Yu W. Characterization of surface emg signal based on fuzzy entropy. IEEE Transaction, 2007. Gibbs J. W. On the equilibrium of heterogeneous substances. Am. J. Sci., 1878. Campbell J. Y. and Shiller R. J. Stock prices, earnings, and expected dividends. The Journal of Finance, 1988. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/99591 