Thermodynamic interpretation of the generalized gravity models with geometry - matter coupling

TL;DR

This paper interprets modified gravity theories with geometry-matter coupling as thermodynamic systems with irreversible matter creation, linking gravitational dynamics to entropy production and particle creation in cosmology.

Contribution

It provides a thermodynamic framework for $f(R,L_m)$ and $f(R,T)$ gravity theories, interpreting their non-conservation as matter creation processes.

Findings

Derivation of particle creation rates and entropy production in these theories

Temperature evolution laws for created particles

Application to a cosmological model showing significant entropy production

Abstract

Modified gravity theories with geometry - matter coupling, in which the action is an arbitrary function of the Ricci scalar and the matter Lagrangian ($f\left(R,L_m\right)$ gravity), and of the Ricci scalar and of the trace of the matter energy-momentum tensor ($f(R,T)$ gravity), respectively, have the intriguing property that the divergence of the matter energy - momentum tensor is nonzero. In the present paper, by using the formalism of open thermodynamic systems, we interpret the generalized conservation equations in these gravitational theories from a thermodynamic point of view as describing irreversible matter creation processes, which could be validated by fundamental particle physics. Thus particle creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents, with the second law of thermodynamics requiring that space-time transforms into matter. The equivalent particle number creation rates, the creation pressure and the entropy production rates are obtained for both $f\left(R,L_m\right)$ and $f(R,T)$ gravity theories. The temperature evolution laws of the newly created particles are also obtained. In the case of the $f(R,T)$ gravity theory the open irreversible thermodynamic interpretation of a simple cosmological model is presented in detail. It is also shown that due to the geometry--matter coupling, during the cosmological evolution a large amount of comoving entropy could be produced.