Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy

TL;DR

This paper derives the most general causal equations for relativistic viscous fluids up to second order in gradients, clarifying the structure of the non-equilibrium entropy current and its thermodynamic constraints.

Contribution

It provides a comprehensive second-order gradient expansion framework for relativistic viscous fluids, including entropy current structure and positivity constraints.

Findings

Derived causal second-order fluid equations

Established relations between entropy current coefficients and equations of motion

Discussed applications to conformal and non-conformal fluids

Abstract

Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains the most general (causal) equations of motion for a fluid in the presence of shear and bulk viscosity, as well as the structure of the non-equilibrium entropy current. Requiring positivity of the divergence of the non-equilibrium entropy current relates some of its coefficients to those entering the equations of motion. I comment on possible applications of these results for conformal and non-conformal fluids.