The generalized second law of gravitational thermodynamics on the   apparent and event horizons in FRW cosmology
  We investigate the validity of the generalized second law of gravitational thermodynamics on the apparent and event horizons in a non-flat FRW universe containing the interacting dark energy with dark matter. We show that for the dynamical apparent horizon, the generalized second law is always satisfied throughout the history of the universe for any spatial curvature and it is independent of the equation of state parameter of the interacting dark energy model. Whereas for the cosmological event horizon, the validity of the generalized second law depends on the equation of state parameter of the model. 
K. Karami, S. Ghaffari and M.M. Soltanzadeh
gr-qc astro-ph.CO hep-th