Relativistic Equilibrium Distribution by Relative Entropy Maximization

TL;DR

This paper derives the relativistic equilibrium distribution using the maximum entropy principle, confirming that the Juttner distribution is the maximum entropy state under Lorentz symmetry, clarifying previous ambiguities.

Contribution

It provides a covariant derivation of the relativistic equilibrium distribution, reaffirming the Juttner distribution as the maximum entropy state with Lorentz invariance.

Findings

Juttner distribution is confirmed as the relativistic maximum entropy state

Covariant formulation clarifies previous confusion about equilibrium states

Reinforces the importance of Lorentz symmetry in relativistic thermodynamics

Abstract

The equilibrium state of a relativistic gas has been calculated based on the maximum entropy principle. Though the relativistic equilibrium state was long believed to be the Juttner distribution, a number of papers have been published in recent years proposing alternative equilibrium states. However, some of these papers do not pay enough attention to the covariance of distribution functions, resulting confusion in equilibrium states. Starting from a fully covariant expression to avoid this confusion, it has been shown in the present paper that the Juttner distribution is the maximum entropy state if we assume the Lorentz symmetry.