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Assessing black swan events with the stochastic least action principle, Tsallis entropy and heavy-tailed distribution

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Abstract

We present a formulation of the Stochastic Least Action Principle which encompasses random movements describing black swan events of non-dissipative systems in terms of heavy-tailed distributions. Black swan events are rare and drastic episodes such as earthquakes and financial crisis. We showed that black swan events of physical systems are proportional to nonlocal correlations, thus making the Tsallis entropy more appropriate for its description rather than the conventional Shannon-Boltzman-Gibbs entropy. As a consequence, we assessed the validity of the path probability distribution obtained using the non-additive Tsallis entropy.

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Data Availability Statement

This manuscript has associated data in a data repository [Authors’ comment: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.]

Notes

  1. This is a kind of mechanical stochastic processes where we can consider the trajectories as markovian chains [3] and compute its path probability.

  2. The fractional derivative is a nonlocal operator, hence long-range interactions and memory effects can be modelled by using the fractional derivative in relation to space or time, respectively [11].

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Acknowledgements

The authors would like to thank the referee for his/her useful comments to improve the physical discussions of the manuscript significantly. This study was funded partially by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. R.B. acknowledges partial support from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq Projects No. 305427/2019–9 and No. 421886/2018–8) and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG Project No. APQ-01142–17).

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Authors and Affiliations

  1. Department of Physics, Federal University of Lavras, Lavras, MG, Brazil

    Tatiana Cardoso e Bufalo, R. Bufalo & Lucas P. G. de Figueiredo

  2. Laboratoire SCIQ, EISEA Numérique et Société, ESIEA Group, Paris, France

    Qiuping A. Wang

  3. Laboratoire IMMM, CNRS, Le Mans University, Le Mans, France

    Qiuping A. Wang

  4. Nanjing University, Nanjing, China

    Fabio Lucio Alves

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  1. Tatiana Cardoso e Bufalo
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Correspondence to R. Bufalo.

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e Bufalo, T.C., Bufalo, R., de Figueiredo, L.P.G. et al. Assessing black swan events with the stochastic least action principle, Tsallis entropy and heavy-tailed distribution. Eur. Phys. J. Plus 138, 282 (2023). https://doi.org/10.1140/epjp/s13360-023-03859-9

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