  We discuss the generalized second law of thermodynamics in three different
systems by taking quantum corrections (logarithmic and power law) to
cosmological horizon entropy as well as black hole entropy. Firstly, we
consider phantom energy accretion onto the Schwarzschild black hole in the
closed FRW universe and investigate validity of the generalized second law of
thermodynamics on the apparent and event horizons. In another scenario, we
evaluate the critical mass of the Schwarzschild black hole with upper and lower
bounds under accretion process due to phantom-like modified generalized
chaplygin gas. It is found that the generalized second law of thermodynamics is
respected within these bounds and black hole cannot accrete outside them.
Finally, we explore this law for a closed universe filled with interacting
$n$-components of fluid (in thermal equilibrium case) and with non-interacting
dark matter and dark energy components (in thermal non-equilibrium case) on the
apparent and event horizons and find conditions for its validity.
