Statistical mechanics in the context of special relativity II

TL;DR

This paper develops a relativistic extension of classical statistical mechanics by generalizing the Boltzmann-Gibbs-Shannon entropy through Lorentz transformations, resulting in a new distribution with power-law tails consistent with experiments.

Contribution

It introduces a Lorentz-invariant generalization of entropy and statistical mechanics, leading to a relativistic distribution function and kinetic theory consistent with special relativity.

Findings

Derived a relativistic entropy compatible with Lorentz transformations.

Obtained a distribution with power-law tails matching experimental data.

Formulated a generalized kinetic equation obeying the H-theorem.

Abstract

The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various physical observables (e.g. momentum, energy, etc), as well as the mathematical apparatus of the theory. Here, following the general lines of [Phys. Rev. E {\bf 66}, 056125 (2002)], we show that the Lorentz transformations impose also a proper one-parameter generalization of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits to construct a coherent and selfconsistent relativistic statistical theory, preserving the main features of the ordinary statistical theory, which recovers 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. Furthermore the new statistical mechanics can be obtained as stationary case of a generalized kinetic theory governed by an evolution equation obeying the H-theorem and reproducing the Boltzmann equation of the ordinary kinetics in the classical limit.