Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy

TL;DR

This work derives the most general relativistic viscous fluid dynamics framework up to second order in gradients for zero chemical potential, detailing the energy-momentum tensor and non-equilibrium entropy current for both conformal and non-conformal fluids. It shows how positivity of the entropy production fixes several second-order transport coefficients and constrains the entropy-current structure, while providing Kubo-type formulas to relate these coefficients to quantum field theory correlators. The results connect fluid-dynamic transport data with holographic (AdS/CFT) expectations and offer a path to extracting second-order coefficients from field theories, with implications for heavy-ion phenomenology and neutron-star physics. Remaining ambiguities (notably an undetermined parameter in the conformal entropy current) point to further theoretical and possible experimental exploration of non-equilibrium entropy production in relativistic 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.