On the Relativistic Micro-Canonical Ensemble and Relativistic Kinetic Theory for N Relativistic Particles in Inertial and Non-Inertial Rest Frames

TL;DR

This paper introduces a new relativistic classical mechanics framework to define micro-canonical ensembles and kinetic theory for N particles, applicable in inertial and non-inertial frames, and explores their non-relativistic limits and fluid dynamics.

Contribution

It provides a novel formulation of relativistic micro-canonical ensembles and kinetic theory based on Poincaré generators, extending classical concepts to relativistic and non-inertial contexts.

Findings

Defined relativistic micro-canonical partition function using Poincaré generators

Established the relativistic one-particle distribution function and Boltzmann equation

Connected relativistic and non-relativistic ensembles through limiting procedures

Abstract

A new formulation of relativistic classical mechanics allows a revisiting of old unsolved problems in relativistic kinetic theory and in relativistic statistical mechanics. In particular a definition of the relativistic micro-canonical partition function is given strictly in terms of the Poincar\'e generators of an interacting N-particle system both in the inertial and non-inertial rest frames. The non-relativistic limit allows a definition of both the inertial and non-inertial micro-canonical ensemble strictly in terms of the Galilei generators. Also the one-particle relativistic distribution function is defined and a new approach to the relativistic Boltzmann equation is delineated. Finally there are some comments on relativistic dissipative fluids.