Derivation of a Relativistic Boltzmann Distribution

TL;DR

This paper develops a relativistic thermodynamics framework by deriving a Boltzmann distribution consistent with Einstein's energy-momentum relation, revealing new insights into temperature, partition functions, and potential gauge theories.

Contribution

It introduces a novel derivation of the relativistic Boltzmann distribution using symmetry principles and PDEs, linking thermodynamics with field theory and gravity-like gauge structures.

Findings

Extended Boltzmann distribution implies inverse four-temperature.

Partition function PDE suggests a quantizable classical statistical field theory.

Framework leads to a thermodynamic certainty relationship.

Abstract

A framework for relativistic thermodynamics and statistical physics is built by first exploiting the symmetries between energy and momentum in the derivation of the Boltzmann distribution, then using Einstein's energy-momentum relationship to derive a PDE for the partition function. It is shown that the extended Boltzmann distribution implies the existence of an inverse four-temperature, while the form of the partition function PDE implies the existence of a quantizable field theory of classical statistics, with hints of an associated gravity like gauge theory. An adaptation of the framework is then used to derive a thermodynamic certainty relationship.