Assuming the universe as a thermodynamical system, the second law of thermodynamics can be extended to another form including the sum of matter and horizon entropies, which is called the generalized second law of thermodynamics. The generalized form of the second law (GSL) is universal which means it holds both in non-equilibrium and equilibrium pictures of thermodynamics. Considering the universe is bounded by a dynamical apparent horizon, we investigate the nature of entropy function for the validity of GSL in the scalar–tensor–vector (STEVE) theory of gravity.

This work is devoted to studying the generalized nature of the entropy function in a specific form of the scalar-tensor-vector (STeVe) theory of gravity for the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in the state of thermal equilibrium. For this purpose, we define an equilibrium picture of thermodynamics by making use of a suitable set of the dark energy density and dark pressure descriptions, which defines an energy-momentum tensor obeying the local energy conservation law. Furthermore, we also discuss our results numerically in order to get additional implications.