We discuss the thermodynamical behavior of homogeneous and isotropic universe (flat and non-flat) in the framework of [Formula: see text] gravity, where [Formula: see text] stands for Ricci scalar and [Formula: see text] signifies the trace of energy–momentum tensor of a scalar field [Formula: see text]. We follow through the first-order formalism that specifies the scalar field to the Hubble parameter which becomes [Formula: see text] By using Bekenstein–Hawking entropy, we analyze the validity of generalized second law of thermodynamics at apparent horizon for different values of [Formula: see text] and evaluate the equilibrium condition for all cases as well.