Statistical approaches on the apparent horizon entropy and the generalized second law of thermodynamics

In this work we have investigated the effects of three nongaussian entropies, namely, modified R\'enyi entropy (MRE), Sharma-Mittal (SME) and dual Kaniadakis (DKE) in investigation generalized second law (GSL) thermodynamics violation. The GSL is an extension for black holes. Recently, it was concluded that a total sum enclosed by apparent horizon plus itself when described Barrow entropy. It assumed universe filled with matter dark energy fluids. Here, will be MRE, SME, then DKE proposals. Since holds usual entropy, but conditionally violated extended implies parameter these entropies should constrained small values order to satisfied. Hence, established conditions where can or cannot obeyed considering statistical concepts just as made Barrow's Considering $\Lambda CDM$ cosmology observe SME DKE, not redshift values.