  Cosmological adiabatic particle creation results in the generation of
irreversible entropy. The evolution of this entropy is examined in a flat
Friedmann--Robertson--Walker universe at late times, using a dissipative model
with a power-law term (proportional to the power of the Hubble parameter $H$).
In a dissipative universe, the irreversible entropy included in the Hubble
volume is found to be proportional to $H^{-1}$, unlike for the case of the
Bekenstein--Hawking entropy on the horizon of the universe. In addition, the
evolution of the horizon entropy is examined, extending the previous analysis
of a non-dissipative universe [Phys.\ Rev.\ D \textbf{100}, 123545 (2019)
(arXiv:1911.08306)]. In the present model, the generalized second law of
thermodynamics is always satisfied, whereas the maximization of entropy is
satisfied under specific conditions. The dissipative universe should be
constrained by the entropy maximization as if the universe behaves as an
ordinary, isolated macroscopic system. The thermodynamic constraints are likely
to be consistent with constraints on a transition from a decelerating universe
to an accelerating universe.
