  We investigate thermodynamics of the apparent horizon in $f(R)$ gravity in
the Palatini formalism with non-equilibrium and equilibrium descriptions. We
demonstrate that it is more transparent to understand the horizon entropy in
the equilibrium framework than that in the non-equilibrium one. Furthermore, we
show that the second law of thermodynamics can be explicitly verified in both
phantom and non-phantom phases for the same temperature of the universe outside
and inside the apparent horizon.
