Generalized Second Law and Thermodynamical Aspects of $f(Q,\mathcal{T})$ Gravity

TL;DR

The paper addresses whether modified gravity in the class $f(Q,\mathcal{T})$ can be thermodynamically viable by formulating the first and generalized second laws at the apparent horizon in a flat FLRW setting. It derives the modified field equations, horizon temperature, and a generalized horizon entropy dependent on $f_Q$, then computes the total entropy rate $\dot{S}_{\rm tot}=\dot{S}_h+\dot{S}_m$ to test the generalized second law. Through five explicit models (linear, power-law, quadratic, exponential, and cross-coupling), it shows linear and mildly nonlinear forms generally satisfy GSLT, while strongly nonlinear or interacting forms require careful parameter tuning. The results demonstrate that thermodynamic consistency acts as a powerful discriminator for the viability of $f(Q,\mathcal{T})$ cosmologies, with implications for explaining late-time cosmic acceleration and guiding model-building.

Abstract

Late-time cosmic acceleration has motivated the exploration of various extensions of general relativity, among which $f(Q,\mathcal{T})$ gravity, based on the non-metricity scalar $Q$ and the trace of the energy--momentum tensor $\mathcal{T}$, has gained increasing attention. In this study, we explore the thermodynamic aspects of $f(Q,\mathcal{T})$ gravity by establishing the first law and generalized second law of thermodynamics at the apparent horizon of a flat FLRW universe. By applying the Gibbs relation, we determined the rate of change of the total entropy and assessed the conditions under which the generalized second law remains valid for various choices of $f(Q,\mathcal{T})$. Our analysis focuses on linear, power-law, quadratic trace, exponential, and cross-coupling models, inspired by frameworks such as $f(R,\mathcal{T})$, $f(T)$, and modifications motivated by string theory. Our analysis showed that linear and mildly nonlinear models are generally thermodynamically consistent, whereas strongly nonlinear or interaction-type models require fine-tuned parameters for the generalized second law to hold. The present analysis underscores that thermodynamic considerations serve as effective criteria for assessing the viability of modified gravity models and their relevance to cosmological dynamics.