Effect of arbitrary matter-geometry coupling on thermodynamics in f(R)theories of gravity

In this paper,the thermodynamics of the Friedmann–Lemait re–Robertson–Walker universe have been explored in f(R)theories of gravity with arbitrary matter-geometry coupling.The equivalence between the modified Friedmann equations with any spatial curvature and the first law of thermodynamics is confirmed,where the assumption of the entropy plays a crucial role.Then laws of thermodynamics in our considering case are obtained.They can reduce to the ones given in Einstein's general theory of relativity under certain conditions.Moreover,a particular model is investigated through the obtained generalized second law of thermodynamics with observational results of cosmographic parameters.