Constraints on the second order transport coefficients of an uncharged fluid

TL;DR

This paper investigates how the requirement of a non-negative entropy current constrains the second order transport coefficients in an uncharged relativistic fluid, reducing their number from fifteen to ten.

Contribution

It derives specific relations among second order transport coefficients based on entropy considerations, refining the understanding of fluid dynamics constraints.

Findings

Entropy current positivity imposes five relations among 15 coefficients.

The stress tensor of an uncharged fluid has 10 independent second order transport coefficients.

Provides a systematic approach to constrain fluid transport properties using entropy conditions.

Abstract

In this note we have tried to determine how the existence of a local entropy current with non-negative divergence constrains the second order transport coefficients of an uncharged fluid, following the procedure described in \cite{Romatschke:2009kr}. Just on symmetry ground the stress tensor of an uncharged fluid can have 15 transport coefficients at second order in derivative expansion. The condition of entropy-increase gives five relations among these 15 coefficients. So finally the relativistic stress tensor of an uncharged fluid can have 10 independent transport coefficients at second order.