Reconstructing f(R,T) gravity from nonequilibrium thermodynamics of spacetime

We show that the field equation for [Formula: see text] gravity can be derived by incorporating an additional entropy production term associated with the geometry-matter coupling. In such nonequilibrium setting, the horizon entropy depends on a general function not only of the Ricci scalar but also of the trace of the stress–energy tensor. We further investigate the homogeneous and isotropic fluid collapse in a simple [Formula: see text] modified gravity model. The conditions for the formation of black holes or naked singularities are discussed.