Classical relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated reference frame

TL;DR

This paper analyzes a classical relativistic ideal gas in thermodynamic equilibrium within a uniformly accelerated frame, deriving explicit distributions and properties consistent with relativistic kinetic theory, including non-relativistic and ultrarelativistic limits.

Contribution

It provides explicit expressions for particle, energy, and entropy densities, as well as total quantities and the center of mass position, extending thermodynamic analysis to accelerated frames.

Findings

Distributions match relativistic Boltzmann kinetic theory results.

Explicit formulas for total entropy, energy, and rest mass.

Phase space volume calculated in ultrarelativistic limit.

Abstract

A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using these methods explicit expressions for the particle, energy and entropy density distributions are obtained, which are found to be in agreement with the well known results of the relativistic formulation of Boltzmann's kinetic theory. Explicit expressions for the total entropy, total energy and rest mass of the gas are obtained. The position of the center of mass of the gas in equilibrium is found. The non-relativistic and ultrarelativistic approximations are also considered. The phase space volume of the system is calculated explicitly in the ultrarelativistic approximation.