Galilean limit of equilibrium relativistic mass distribution for indistinguishable events

TL;DR

This paper explores the transition from relativistic to nonrelativistic statistical mechanics for indistinguishable events, analyzing thermodynamic quantities in the Galilean limit and confirming consistency with classical mechanics.

Contribution

It introduces a relativistic mass distribution framework for indistinguishable events and demonstrates its reduction to classical statistical mechanics in the Galilean limit.

Findings

Thermodynamic quantities match relativistic kinetic theory at limits.

Galilean limit reproduces nonrelativistic statistical mechanics.

Results confirm consistency across relativistic and classical regimes.

Abstract

The relativistic distribution for indistinguishable events is considered in the mass-shell limit $m^2\cong M^2,$ where $M$ is a given intrinsic property of the events. The characteristic thermodynamic quantities are calculated and subject to the zero-mass and the high-temperature limits. The results are shown to be in agreement with the corresponding expressions of an on-mass-shell relativistic kinetic theory. The Galilean limit $c\rightarrow \infty ,$ which coincides in form with the low-temperature limit, is considered. The theory is shown to pass over to a nonrelativistic statistical mechanics of indistinguishable particles.