Cosmological thermodynamics with Hawking temperature on the apparent horizon and Unruh temperature of the fluid: Some interesting consequences

Thermodynamics on the cosmological apparent horizon of a flat Friedmann-Lemaitre-Robertson-Walker metric has been investigated with Bekenstein entropy and Hawking temperature on the horizon, and Unruh temperature for the fluid inside the horizon. This temperature is experienced by a radial comoving observer infinitesimally close to the horizon due to the pressure exerted by the fluid bounded by the horizon. An expression for the entropy of the fluid has been obtained which is found to be proportional to the volume of the thermodynamic system which implies that the Unruh temperature of the fluid is inconsistent with the holographic principle. Further, we have been able to find an expression for the effective entropy of the system. Finally, assuming a barotropic equation of state $p=w\rho$ ($w$ constant) for the fluid, it has been shown that the generalized second law holds good for a non-phantom w, while thermodynamic equilibrium is never possible for such a scenario.