In this paper we study the recently proposed $f(R,\mathcal{L})$ theories from a thermodynamic point of view. The uniqueness of these theories lies in the fact that the space-time curvature is coupled to the baryonic matter instead of exotic matter (in the form of scalar field). We investigate the viability of these theories from the point of view of the thermodynamic stability of the models. To be more precise here we are concerned with the thermodynamics of the apparent horizon of Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in the background of the $f(R,\mathcal{L})$ theory. We consider several models of $f(R,\mathcal{L})$ theories where both minimal and nonminimal coupling has been considered. Various thermodynamic quantities like entropy, enthalpy, internal energy, Gibbs free energy, etc. are computed and using their allowed ranges various model parameters are constrained.

• Received 14 January 2020
• Revised 13 February 2020
• Accepted 9 April 2020

DOI:https://doi.org/10.1103/PhysRevD.101.084057