Thermodynamics in $f(T)$ Gravity and Corrected Entropies

TL;DR

This study investigates the validity of the generalized second law of thermodynamics in $f(T)$ gravity using quantum-corrected entropies on different horizons, finding it holds under certain conditions for power-law corrections but not for logarithmic ones.

Contribution

It introduces a specific $f(T)$ gravity model considering quantum entropy corrections and analyzes the law's validity on multiple horizons.

Findings

Generalized second law holds with power-law corrected entropy within specific parameters.

Law is violated for all parameters with logarithmic corrected entropy.

Different horizons exhibit distinct thermodynamic behaviors in $f(T)$ gravity.

Abstract

This paper is devoted to study the generalized second law of thermodynamics in $f(T)$ gravity. We use quantum corrections such as power-law and logarithmic corrected entropies to the horizon entropy along with Gibbs' equation in the thermal equilibrium state. We derive $f(T)$ model by taking into account a power-law scale factor through the first modified Friedmann equation which obeys the condition for a realistic model. Two types of horizons, i.e., Hubble and event horizons are used to check the validity of the generalized second law of thermodynamics with corrected entropies. We conclude that this law holds with a specific range of entropy parameter on both horizons in the case of power-law corrected entropy, while it violates for all values of entropy parameter on both horizons for logarithmic corrected entropy.