On the local thermodynamic relations in relativistic spin hydrodynamics

TL;DR

This paper shows that traditional local thermodynamic relations used in relativistic spin hydrodynamics are invalid even at global equilibrium, due to quantum corrections in pressure derivatives related to spin potential.

Contribution

It provides a rigorous quantum statistical analysis demonstrating the failure of standard thermodynamic relations in relativistic spin hydrodynamics at equilibrium.

Findings

Derivative of pressure w.r.t. spin potential differs from spin density.

Quantum corrections cannot be removed by entropy-gauge transformations.

Traditional thermodynamic assumptions are invalid for accurate constitutive relations.

Abstract

We demonstrate, by providing two specific examples, that the local differential thermodynamic relations used as educated guesses in relativistic hydrodynamics with spin, do not hold even at global thermodynamic equilibrium. We show, by using a rigorous quantum statistical method, that for massless free fermions and massive free fermions with rotation and acceleration at global thermodynamic equilibrium, the derivative of the pressure function with respect to the spin potential differs from the spin density and acquires a correction of the same order. Such correction cannot be eliminated by any redefinition of the entropy current, a so-called entropy-gauge transformation. Therefore, for an accurate determination of the constitutive relations in relativistic spin hydrodynamics, the traditional method of assuming differential thermodynamic relations is not appropriate.