# Equilibrium thermodynamic susceptibilities for a dense degenerate Dirac field

## TL;DR

This paper calculates second order thermodynamic susceptibilities for a free massive Dirac field at zero temperature and nonzero chemical potential, providing explicit formulas and constitutive relations relevant for relativistic fluid dynamics.

## Contribution

It provides the first explicit computation of all parity-even second order thermodynamic susceptibilities for a free massive Dirac field in this regime.

## Key findings

- Explicit formulas for second order susceptibilities at zero temperature.
- Constitutive relations for energy-momentum tensor and current.
- Application of Kubo formulas to relativistic fermionic systems.

## 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.