Equilibrium partition function for nonrelativistic fluids

TL;DR

This paper develops an equilibrium partition function for non-relativistic fluids by reducing relativistic fluids via light cone reduction, establishing a precise correspondence between null and non-relativistic fluids in terms of symmetries and thermodynamics.

Contribution

It introduces a method to derive non-relativistic fluid dynamics from relativistic fluids using light cone reduction, providing a detailed match of their thermodynamic and symmetry properties.

Findings

Null fluid symmetry matches non-relativistic fluid symmetry

Equilibrium partition functions are equivalent to all orders in derivatives

Relativistic and non-relativistic fluids share thermodynamic relations

Abstract

We construct an equilibrium partition function for a non-relativistic 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 Poincare 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 non-relativistic fluid. In particular, their symmetries, thermodynamics, constitutive relations, and equilibrium partition function match exactly to all orders in derivative expansion.