Towards a relativistic statistical theory

TL;DR

This paper introduces a relativistic extension of classical statistical mechanics by deforming the Boltzmann-Gibbs-Shannon entropy with a parameter linked to light speed, resulting in a distribution with power-law tails consistent with experiments.

Contribution

It develops a coherent relativistic statistical theory by deforming classical entropy, preserving key thermodynamic features and aligning with experimental power-law distributions.

Findings

Relativistic entropy is a one-parameter deformation of classical entropy.

Derived distribution exhibits power-law tails matching experimental data.

The theory maintains classical features like maximum entropy and stability.

Abstract

In special relativity the mathematical expressions, defining physical observables as the momentum, the energy etc, emerge as one parameter (light speed) continuous deformations of the corresponding ones of the classical physics. Here, we show that the special relativity imposes a proper one parameter continuous deformation also to the expression of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits to construct a coherent and selfconsistent relativistic statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002); Phys. Rev. E {\bf 72}, 036108 (2005)], preserving the main features (maximum entropy principle, thermodynamic stability, Lesche stability, continuity, symmetry, expansivity, decisivity, etc.) of the classical statistical theory, which is recovered in the classical limit. The predicted distribution function is a one-parameter continuous deformation of the classical Maxwell-Boltzmann distribution and has a simple analytic form, showing power law tails in accordance with the experimental evidence.