Thermodynamics of a morphological transition in a relativistic gas

TL;DR

This paper develops a thermodynamic framework to analyze a critical morphological transition in relativistic gases, deriving phase transition characteristics and confirming results with numerical solutions.

Contribution

It introduces a thermodynamic potential approach to describe the phase transition in relativistic gases, providing new insights and predictions.

Findings

Critical exponents calculated for the transition

Thermodynamic potential explains spontaneous order emergence

Numerical solutions confirm the theoretical framework

Abstract

Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to such a critical phenomenon. We therefore construct a thermodynamic potential which upon expansion leads to Landau-like (mean-field) theory of phase transition. We are therefore able to calculate critical exponents and explain the spontaneous emergence of order parameter as a result of relativistic constraints. Numerical solutions which confirm our thermodynamic approach are also provided. Our approach provides a general understanding of such a transition as well as leading to some new results. Finally, we briefly discuss some possible physical consequences of our results as well as considering the case of quantum relativistic gases.