The generalized second law of thermodynamics and the nature of the Entropy Function

TL;DR

This paper investigates the form of the entropy function necessary for the generalized second law of thermodynamics to hold in a universe bounded by an event horizon, considering different cosmic eras and arbitrary entropy functions.

Contribution

It explores the nature of the entropy function on the event horizon for the validity of the GSLT without assuming the Bekenstein-Hawking relation.

Findings

Entropy function varies with cosmic era.

Graphical analysis illustrates entropy behavior.

GSLT holds under specific entropy functions.

Abstract

In black hole physics, the second law of thermodynamics is generally valid whether the black hole is a static or a non-static one. Considering the universe as a thermodynamical system the second law of black hole dynamics extends to the non-negativity of the sum of the entropy of the matter and the horizon, known as generalized second law of thermodynamics(GSLT). Here, we have assumed the universe to be bounded by the event-horizon where Bekenstein entropy-area relation and Hawking-temperature are not applicable. Thus considering entropy to be an arbitrary function of the area of the event-horizon, we have tried to find the nature of the entropy-function for the validity of the GSLT both in quintessence-era and in phantom-era. Finally, some graphical representation of the entropy-function has been presented.