# Thermodynamics in a Modified Gravity Involving Higher-Order Torsion Derivative Terms

## TL;DR

This paper investigates the thermodynamical laws in a modified teleparallel gravity with higher-order torsion derivatives, analyzing equilibrium and non-equilibrium scenarios, and confirming the generalized second law of thermodynamics under certain conditions.

## Contribution

It introduces a novel analysis of thermodynamics in higher-order torsion gravity, including the first law, GSLT, and entropy corrections, in both equilibrium and non-equilibrium frameworks.

## Key findings

- Non-equilibrium thermodynamics with entropy production exists in this theory.
- GSLT holds within specific parameter ranges for different models.
- Logarithmic entropy corrections are compatible with GSLT validity.

## Abstract

The present study is elaborated to investigate the validity of thermodynamical laws in a modified teleparallel gravity based on higher-order derivatives terms of torsion scalar. For this purpose, we consider spatially flat FRW model filled with perfect fluid matter contents. Firstly, we explore the possibility of existence of equilibrium as well as non-equilibrium picture of thermodynamics in this extended version of teleprallel gravity. Here, we present the first law and the generalized second law of thermodynamics (GSLT) using Hubble horizon. It is found that non-equilibrium description of thermodynamics exists in this theory with the presence of an extra term called as entropy production term. We also establish GSLT using the logarithmic corrected entropy. Further, by taking the equilibrium picture, we discuss validity of GSLT at Hubble horizon for two $F$ different models. Using Gibbs law and the assumption that temperature of matter within Hubble horizon is similar to itself, we use different cases for choices scale factors to discuss the GSLT validity graphically in all scenarios. It is found that the GSLT is satisfied for a specified range of free parameters in all cases.