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Tsallis Distribution as a Λ-Deformation of the Maxwell-Jüttner Distribution
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: Received: 28 February 2024 / Approved: 29 February 2024 / Online: 29 February 2024 (13:00:14 CET)
A peer-reviewed article of this Preprint also exists.
Gazeau, J.-P. Tsallis Distribution as a Λ-Deformation of the Maxwell–Jüttner Distribution. Entropy 2024, 26, 273. Gazeau, J.-P. Tsallis Distribution as a Λ-Deformation of the Maxwell–Jüttner Distribution. Entropy 2024, 26, 273.
Abstract
Currently, there is no widely accepted consensus regarding a consistent thermodynamic framework within the special relativity paradigm. However, by postulating that the inverse temperature 4-vector, denoted as β, is future-directed and timelike, intriguing insights emerge. Specifically, it is demonstrated that the q-dependent Tsallis distribution can be conceptualized as a de-Sitterian deformation of the relativistic Maxwell-Jüttner distribution. In this context, the curvature of the de Sitter space-time is characterized by Λ/3, where Λ represents the cosmological constant within the ΛCDM standard model for Cosmology. For a simple gas composed of particles with proper mass m, and within the framework of quantum statistical de Sitterian considerations, the Tsallis parameter q exhibits a dependence on the cosmological constant given by q=1+ℓcΛ/n where ℓc=ℏ/mc is the Compton length of the particle and n is a positive numerical factor. This formulation establishes a novel connection between the Tsallis distribution, quantum statistics, and the cosmological constant, shedding light on the intricate interplay between relativistic thermodynamics and fundamental cosmological parameters.
Keywords
Maxwell-Jüttner distribution; Tsallis distribution; de Sitter quantum field; ΛCDM standard model
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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