<p>Numerous models have been proposed theoretically to explain the observed phenomena of the accelerated expansion of the current cosmology. Among these, f(R) gravity theories emerge as a competitive framework, as they not only account for the observed acceleration but also provide an explanation for the early inflation of the cosmology. To further investigate the validity of these theories, we investigate coupled f(R) gravitational models from the perspective of thermodynamics, under the assumption of non-minimal coupling between matter and geometry. This paper explores the thermodynamic properties of three different f(R) forms of gravitational models on cosmological scales, deriving their corresponding entropy functions and applying the generalized second law of thermodynamics. Finally, by employing the generalized second law of thermodynamics and analyzing relevant astronomical observation data, the model parameters for these three f(R) gravitational models are constrained. The results of these constraints not only identify the parameter ranges that satisfy the thermodynamic requirements but also point to matter candidates that realize the accelerated expansion of the cosmology.</p>