• Rapid Communication

Thermodynamics from first principles: Correlations and nonextensivity

S. N. Saadatmand, Tim Gould, E. G. Cavalcanti, and J. A. Vaccaro
Phys. Rev. E 101, 060101(R) – Published 1 June 2020
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Abstract

The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this Rapid Communication, we use the fundamental principles of ergodicity (via Liouville's theorem), the self-similarity of correlations, and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long-range-interacting systems. Significantly, our formalism provides a justification for the well-studied nonextensive thermostatistics characterized by the Tsallis distribution, which it includes as a special case. We also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the Gibbs-Shannon entropy. The consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics.

  • Figure
  • Received 10 July 2019
  • Revised 16 March 2020
  • Accepted 8 May 2020

DOI:https://doi.org/10.1103/PhysRevE.101.060101

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. N. Saadatmand1,*, Tim Gould2, E. G. Cavalcanti3, and J. A. Vaccaro1

  • 1Centre for Quantum Dynamics, Griffith University, Nathan QLD 4111, Australia
  • 2Qld Micro- and Nanotechnology Centre, Griffith University, Nathan QLD 4111, Australia
  • 3Centre for Quantum Dynamics, Griffith University, Gold Coast QLD 4222, Australia

  • *n.saadatmand@griffith.edu.au

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Issue

Vol. 101, Iss. 6 — June 2020

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