Thermodynamics of ideal spin fluids and pseudo-gauge ambiguity

TL;DR

This paper investigates how different pseudo-gauge choices affect the thermodynamics of ideal spin fluids, establishing universal relations and applying them to free Dirac fermions and scalar fields.

Contribution

It systematically analyzes pseudo-gauge ambiguities in ideal spin hydrodynamics and derives universal thermodynamic relations applicable across pseudo-gauges.

Findings

Identifies pseudo-gauge choices satisfying standard thermodynamic relations.

Quantifies ambiguities in the spin equation of state.

Derives universal thermodynamic relations for conserved currents.

Abstract

Conserved currents of relativistic spin fluids derived from microscopic models are known to violate local thermodynamic relations. We present a systematic analysis of pseudo-gauge improvements in ideal spin hydrodynamics and identify a family of pseudo-gauges where standard thermodynamic relations are satisfied. We quantify pseudo-gauge ambiguities in the spin equation of state and derive universal thermodynamic relations that apply to conserved currents in any pseudo-gauge. As an application, we extract the thermodynamic variables and equations of state for free Dirac fermions and scalar fields.