Temperature in relativistic fluids

Abstract

For static matter in a gravitational field, different conventions for equilibrium local temperature exist in the classic physics literature. We illustrate the difference between two popular conventions using black-body radiation in a spherically symmetric gravitational potential. Equilibrium temperatures defined by the "Landau frame" or "Eckart frame" prescriptions most commonly used in relativistic fluid dynamics do not satisfy the statistical-mechanical relation $1/T=dS/dE$.

arXiv comment14 pages, 3 figures. V2: Small clarifications, version accepted for publication in PRD

References in corpus (17)

• Nonlinear Fluid Dynamics from Gravity
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Constraints on Fluid Dynamics from Equilibrium Partition Functions
• Towards hydrodynamics without an entropy current
• Spectral sum rules for the quark-gluon plasma
• Parity-Violating Hydrodynamics in 2+1 Dimensions
• Kubo Formulae for Second-Order Hydrodynamic Coefficients
• General equilibrium second-order hydrodynamic coefficients for free quantum fields
• Relaxation time of a CFT plasma at finite coupling
• Thermodynamical second-order hydrodynamic coefficients
• Tolman temperature gradients in a gravitational field
• Second order hydrodynamic coefficients from 3-point stress tensor correlators via AdS/CFT
• The second order hydrodynamic transport coefficient $\kappa$ for the gluon plasma from the lattice
• Kubo formulas for thermodynamic transport coefficients
• Second-order partition function of a non-interacting chiral fluid in 3+1 dimensions
• Analytic Transport from Weak to Strong Coupling in the O(N) model
• On the Gravitational Wave to Matter Coupling of Superfluid Fermi Gases Near Unitarity

Cited by in corpus (6)

• Causal and stable first-order chiral hydrodynamics
• Linear stability analysis in inhomogeneous equilibrium configurations
• Leading order magnetic field dependence of conductivities in anomalous hydrodynamics
• Heat propagation in rotating relativistic bodies
• Causal and Stable Superfluid Hydrodynamics
• Thermoelectric Conduction in General Relativity: A Causal, Stable, and Well Posed Theory