The generalized second law of thermodynamics with Barrow entropy

TL;DR

This paper examines the validity of the generalized second law of thermodynamics using Barrow entropy, revealing potential violations depending on the universe's evolution and the deformation parameter.

Contribution

It introduces Barrow entropy into the thermodynamic analysis of the universe and explores conditions under which the generalized second law holds or is violated.

Findings

For standard entropy, the law always holds.

Barrow entropy can lead to violations of the law.

Small deviations from standard entropy prevent violations.

Abstract

We investigate the validity of the generalized second law of thermodynamics, applying Barrow entropy for the horizon entropy. The former arises from the fact that the black-hole surface may be deformed due to quantum-gravitational effects, quantified by a new exponent $\Delta$. We calculate the entropy time-variation in a universe filled with the matter and dark energy fluids, as well as the corresponding quantity for the apparent horizon. We show that although in the case $\Delta=0$, which corresponds to usual entropy, the sum of the entropy enclosed by the apparent horizon plus the entropy of the horizon itself is always a non-decreasing function of time and thus the generalized second law of thermodynamics is valid, in the case of Barrow entropy this is not true anymore, and the generalized second law of thermodynamics may be violated, depending on the universe evolution. Hence, in order not to have violation, the deformation from standard Bekenstein-Hawking expression should be small as expected.