# Thermodynamics of uncharged relativistic multifluids

## TL;DR

This paper develops a thermodynamic framework for uncharged relativistic multifluids, particularly applied to superfluid neutron star interiors, clarifying the interpretation of variables and gauge freedoms in hydrodynamic models.

## Contribution

It provides a thermodynamic interpretation of Carter's multifluid formalism, clarifies gauge freedoms, and connects various models used in superfluid neutron star studies.

## Key findings

- Thermodynamic equilibrium reduces the number of state variables.
- Gauge freedom simplifies the hydrodynamic formulation.
- Affinity and reaction concepts remain valid with superfluid currents.

## Abstract

The internal layers of neutron stars are expected to contain several superfluid components that can significantly affect their dynamics. The description of such objects should rely on hydrodynamic models in which it is possible to unambiguously assign the value of the thermodynamic variables from microscopic calculations of the properties of matter. In this work we consider the phenomenological approach to multifluids modelling championed by Carter and, studying the relaxation of the system towards equilibrium, we assign a precise thermodynamic interpretation to its variables. We show that in thermodynamic equilibrium the equation of state contains less state variables than those needed in the phenomenological model, implying the existence of a gauge freedom of the theory that can be used to simplify the hydrodynamic formulation in the non-dissipative limit. Once this is understood, it becomes easy to translate the different multifluid formalisms that have been proposed in the literature into Carter's form. Finally, we show that the usual concepts of affinity and reaction coordinates, as they are introduced in chemistry, are not affected by the presence of superfluid currents. In an effort to make the concepts clear, the formalism is developed step-by-step from first principles, providing model examples and several applications of practical relevance for the study of superfluid neutron star interiors.