Constraints on the second order transport coefficients of an uncharged fluid

TL;DR

This work analyzes how a local entropy current with non-negative divergence constrains second-order transport coefficients in an uncharged relativistic fluid in 3+1 dimensions, showing symmetry allows 15 structures but positivity yields five relations, leaving 10 independent coefficients.The authors implement a constructive procedure: classify derivative data under SO(3), build the entropy current up to third order, compute its divergence up to fourth order, and enforce positivity to derive explicit constraints on the second-order constitutive relations, including a detailed conformal limit analysis.They obtain five explicit relations among the 15 second-order coefficients, derive the dependence of the remaining eight on entropy-current parameters, and compare their results to dimen­sionally reduced non-conformal theories and to Romatschke (2009) and Kanitscheider (2009), noting both concordances and a notable discrepancy in a particular combination with Romatschke’s results.Overall, the paper provides a systematic, theory-agnostic framework for constraining second-order relativistic hydrodynamics via the second-law requirement, with implications for modeling near-equilibrium dynamics in heavy-ion collisions and related systems.

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.