Some statistical approaches in the apparent horizon entropy and the generalized second law of thermodynamics

The well known connection between black holes and thermodynamics, as well as their basic statistical mechanics, has been explored during the last decades since the published papers by Hawking, Jacobson and Unruh. In this work we have investigated the effects of three nongaussian entropies which are the modified Renyi entropy (MRE), Sharma-Mittal entropy (SME) and the dual Kaniadakis entropy (DKE) in the investigation of the generalized second law of thermodynamics, an extension of second law for black holes. Recently, it was analyzed that a total entropy is the sum of the entropy enclosed by the apparent horizon plus the entropy of the horizon itself when the apparent horizon is described by the Barrow entropy. It is assumed that the universe is filled with the matter and dark energy fluids. Here, as we said just above, the apparent horizon is described by the MRE and SME entropies, and then by the DKE proposal. We have established conditions where the second law of thermodynamics can or cannot be obeyed in the MRE, the SME as well as in the DKE just as it did in Barrows entropy.