Equilibrium thermodynamic susceptibilities for a dense degenerate Dirac field

Abstract

Parity preserving relativistic fluids in four spacetime dimensions admit seven independent thermodynamic susceptibilities at the second order in the hydrodynamic derivative expansion. We compute all parity-even second order thermodynamic susceptibilities for a free massive Dirac field at zero temperature and a nonzero chemical potential, based on the Kubo formulas reported in P. Kovtun and A. Shukla, Kubo formulas for thermodynamic transport coefficients, J. High Energy Phys. 10 (2018) 007. We also compute the second order constitutive relations for the energy-momentum tensor and the conserved current in the absence of external gauge fields.