Entropic form emergent from superstatistics

Maike A. F. dos Santos, Fernando D. Nobre, and Evaldo M. F. Curado
Phys. Rev. E 107, 014132 – Published 25 January 2023

Abstract

The Beck-Cohen superstatistics became an important theory in the scenario of complex systems because it generates distributions representing regions of a nonequilibrium system, characterized by different temperatures Tβ1, leading to a probability distribution f(β). In superstatistics, some classes have been most frequently considered for f(β), like χ2, χ2 inverse, and log-normal ones. Herein we investigate the superstatistics resulting from a χη2 distribution through a modification of the usual χ2 by introducing a real index η (0<η1). In this way, one covers two common and relevant distributions as particular cases, proportional to the q-exponential (eqβx=[1(1q)βx]11q) and the stretched exponential (e(βx)η). Furthermore, an associated generalized entropic form is found. Since these two particular-case distributions have been frequently found in the literature, we expect that the present results should be applicable to a wide range of classes of complex systems.

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  • Received 19 September 2022
  • Accepted 23 December 2022

DOI:https://doi.org/10.1103/PhysRevE.107.014132

©2023 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Maike A. F. dos Santos1,2,*, Fernando D. Nobre2,3,†, and Evaldo M. F. Curado2,3,‡

  • 1Department of Physics, PUC-Rio, Rua Marquês de São Vicente, 225, 22451-900, Rio de Janeiro, Brazil
  • 2Centro Brasileiro de Pesquisas Físicas Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
  • 3National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil

  • *Corresponding author: santosmaikeaf@gmail.com
  • fdnobre@cbpf.br
  • evaldo@cbpf.br

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Vol. 107, Iss. 1 — January 2023

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