Thermodynamics of ideal spin fluids and pseudo-gauge ambiguity

TL;DR

This work analyzes pseudo-gauge ambiguities in spin hydrodynamics and identifies a class of thermodynamic pseudo-gauges in which standard local thermodynamic relations hold for conserved currents. By deriving thermo-dynamic PDE constraints and gauge-invariant quantities, the authors formulate a spin equation of state that is generally gauge-dependent, except in conformal (scale-invariant) theories where the ambiguity is eliminated. They demonstrate the method with explicit results for massless Dirac fermions and scalar fields, obtaining conformal, spin-sensitive thermodynamic variables and invariants that reconcile microscopic currents with thermodynamics. The study clarifies how to extract thermodynamic information from spin currents and suggests future work on stability, causality, and an action-based route to selecting a preferred pseudo-gauge.

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.