Relativistic kinematic approach to the classical ideal gas

TL;DR

This paper derives a purely kinematic framework for describing a classical ideal gas, reducing the variables needed and providing solutions for its evolution in local thermal equilibrium.

Contribution

It introduces a relativistic kinematic approach to characterize classical ideal gases, simplifying previous hydrodynamic descriptions.

Findings

Derived necessary and sufficient conditions for a unit time-like vector field to represent a classical ideal gas velocity.

Reduced the number of variables needed to describe such gases.

Provided test solutions modeling the gas's evolution in local thermal equilibrium.

Abstract

he necessary and sufficient conditions for a unit time-like vector field to be the unit velocity of a classical ideal gas are obtained. In a recent paper [Coll, Ferrando and S\'aez, Phys. Rev D {\bf 99} (2019)] we have offered a purely hydrodynamic description of a classical ideal gas. Here we take one more step in reducing the number of variables necessary to characterize these media by showing that a plainly kinematic description can be obtained. We apply the results to obtain test solutions to the hydrodynamic equation that model the evolution in local thermal equilibrium of a classical ideal gas. \end{abstract}