Laws of thermodynamic equilibrium within first order relativistic hydrodynamics

TL;DR

This paper generalizes classical thermodynamic equilibrium relations within first order relativistic hydrodynamics, linking them to the fluid's thermal equilibrium state and exploring their dependence on spacetime symmetries.

Contribution

It introduces a generalized weak version of Tolman-Ehrenfest and Klein's laws applicable to relativistic fluids on arbitrary backgrounds, based on the absence of heat flux.

Findings

Derived a generalized relation for temperature and chemical potential in relativistic fluids.

Showed the dependence of classical equilibrium laws on spacetime symmetries.

Demonstrated that stronger equilibrium conditions lead to constant thermodynamic parameters along flow lines.

Abstract

Using recently developed consistent and robust first order relativistic hydrodynamics of a dissipative fluid we propose a generalization but weak version of Tolman-Ehrenfest relation and Klein's law on a general background spacetime. These relations are appeared to be a consequence of thermal equilibrium state of the fluid, defined by the absence of heat flux. We interpret them as the defining relations for the local temperature and chemical potential of the fluid. The validity of usual Tolman-Ehrenfest relation and Klein's law deeply depends on the existence of a global timelike Killing vector. However imposition of more stronger equilibrium condition -- local conservation of entropy current -- yields the constancy of the equilibrium thermodynamic parameters along the flow lines.