Thermodynamic scheme of inhomogeneous perfect fluid mixtures

TL;DR

This paper explores the relationship between thermodynamics and geometrodynamics in inhomogeneous cosmological models, revealing that only highly symmetric models like FRW are compatible with thermodynamic principles.

Contribution

It generalizes the thermodynamic scheme of general relativity to include chemical potential and entropy production in inhomogeneous perfect fluid mixtures.

Findings

Compatibility conditions restrict models to FRW symmetry

Inhomogeneous models generally incompatible with thermodynamics

Chemical potential inclusion affects model compatibility

Abstract

We analyze the compatibility between the geometrodynamics and thermodynamics of a binary mixture of perfect fluids which describe inhomogeneous cosmological models. We generalize the thermodynamic scheme of general relativity to include the chemical potential of the fluid mixture with non-vanishing entropy production. This formalism is then applied to the case of Szekeres and Stephani families of cosmological models. The compatibility conditions turn out to impose symmetry conditions on the cosmological models in such a way that only the limiting case of the Friedmann-Robertson-Walker model remains compatible. This result is an additional indication of the incompatibility between thermodynamics and relativity.