Correspondence between momentum dependent relaxation time and field redefinition of relativistic hydrodynamic theory

TL;DR

This paper establishes a link between momentum-dependent relaxation times and thermodynamic field redefinitions in relativistic hydrodynamics, showing how dissipative effects influence the macroscopic variables and ensuring energy-momentum conservation and entropy production positivity.

Contribution

It introduces a novel correspondence between dissipation and thermodynamic field redefinition via MDRTA, developing a second order relativistic hydrodynamic theory with dissipative effects included.

Findings

Thermodynamic fields are not uniquely defined out of equilibrium.

Energy-momentum conservation is maintained with redefined fields.

Entropy production remains non-negative with positive transport coefficients.

Abstract

In this article a correspondence has been established between the out of equilibrium system dissipation and the thermodynamic field redefinition of the macroscopic variables through the momentum dependent relaxation time approximation (MDRTA) solution of relativistic transport equation. Here, it has been shown that the out of equilibrium thermodynamic fields are not uniquely defined and are subjected to include dissipative effects from the medium. A second order relativistic hydrodynamic theory has been developed including such dissipative effects. The necessary conditions for developing a hydrodynamic theory has been fulfilled, (i) the thermodynamic identities incorporating such redefined fields have been shown to conserve the energy-momentum tensor perfectly under MDRTA, (ii) the non-negativity of entropy production remains unaffected by the inclusion of such dissipative contributions in hydro fields as long as the independent transport coefficients remain positive.