Study of f(R) gravitational models with arbitrary coupling between matter and geometry via generalized second law of thermodynamics

As a member of modified theories of gravity, [Formula: see text] theories of gravity offer a compelling explanation for the observed phenomenon of the late-time cosmic acceleration, which is a puzzle that general relativity cannot solve. Moreover, it has been proved that the field equations of [Formula: see text] theories of gravity are equivalent to the first law of thermodynamics. This equivalence holds true even in the presence of matter-geometry coupling. As more and more [Formula: see text] gravitational models are proposed, it is crucial to investigate their physical validity. In this paper, three different [Formula: see text] gravitational models with arbitrary coupling between matter and geometry are investigated by the generalized second law of thermodynamics on cosmological scales with astronomical observational data. The results show that all the models considered in this work not only satisfy the generalized second law of thermodynamics but also account for the late-time cosmic acceleration. Moreover, the cosmic matter candidates in the models under consideration are radiation, ordinary matter, vacuum energy, quintessence-like fields or phantom-like fields.