Equilibrium partition function for nonrelativistic fluids

Abstract

We construct an equilibrium partition function for a nonrelativistic fluid and use it to constrain the dynamics of the system. The construction is based on light cone reduction, which is known to reduce the Poincaré symmetry to Galilean in one lower dimension. We modify the constitutive relations of a relativistic fluid, and find that its symmetry broken phase—“null fluid” is equivalent to the nonrelativistic fluid. In particular, their symmetries, thermodynamics, constitutive relations, and equilibrium partition function match exactly to all orders in derivative expansion.