Thermodynamics on the horizon of a flat universe at late times is studied in holographic cosmological models that assume an associated entropy on the horizon. In such models, a Λ (t) model similar to a time-varying Λ (t) cosmology is favored because of the consistency of energy flows across the horizon. Based on this consistency, a Λ (t) model with a power-law term proportional to Hα is formulated to systematically examine the evolution of the Bekenstein-Hawking entropy. Here, H is the Hubble parameter and α is a free parameter whose value is a real number. The present model always satisfies the second law of thermodynamics on the orizon. In particular, the universe for α < 2 tends to approach thermodynamic equilibriumlike states. Consequently, when α < 2 , the maximization of the entropy should be satisfied as well, at least in the last stage of the evolution of an expanding universe. A relaxationlike process before the last stage is also examined from a thermodynamics viewpoint.
KOMATSU et al. (Mon,) studied this question.