Causality and thermodynamics in anisotropic fluids

TL;DR

This paper develops a causal thermodynamic formalism for anisotropic imperfect fluids, extending existing theories to incorporate anisotropy while ensuring thermodynamic consistency and causality.

Contribution

It generalizes the Israel-Stewart formalism to include anisotropic effects in a causal thermodynamic framework.

Findings

The formalism recovers Eckart's theory in the isotropic limit.

Explicit derivation of the second law with anisotropy terms.

Framework applicable to both first- and second-order theories.

Abstract

We propose a thermodynamic formalism, within the particle-frame, for the energy-momentum tensor of irreversible anisotropic imperfect fluids subject to causality. Building on the Israel-Stewart extension of Eckart's theory, we further generalize these formalisms to incorporate anisotropic effects while ensuring the preservation of causality. In this framework, the second law of thermodynamics includes an additional term accounting for the system's anisotropy, which we derive explicitly in closed form for both first- and second-order theories. Notably, when anisotropy is removed, our model recovers Eckart's theory at first order and Israel-Stewart's at second order.