  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 non-minimal 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.
