Entropy current and entropy production in relativistic spin hydrodynamics

TL;DR

This paper derives a universal expression for entropy production in relativistic spin hydrodynamics, revealing the non-uniqueness of the entropy current and the invariance of entropy production under gauge transformations.

Contribution

It introduces a first-principle quantum-statistical method to define entropy production and shows its invariance, extending previous literature.

Findings

Entropy current is not uniquely defined and can be gauge-transformed.

Entropy production rate remains invariant under entropy-gauge transformations.

Provides a universally applicable expression for entropy production in relativistic spin hydrodynamics.

Abstract

We use a first-principle quantum-statistical method to derive the expression of the entropy production rate in relativistic spin hydrodynamics. We show that the entropy current is not uniquely defined and can be changed by means of entropy-gauge transformations, much the same way as the stress-energy tensor and the spin tensor can be changed with pseudo-gauge transformations. We show that the local thermodynamic relations, which are admittedly educated guesses in relativistic spin hydrodynamics inspired by those at global thermodynamic equilibrium, do not hold in general and they are also non-invariant under entropy-gauge transformations. Notwithstanding, we show that the entropy production rate is independent of those transformations and we provide a universally applicable expression, extending that known in literature, from which one can infer the dissipative parts of the energy momentum and spin tensors.