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

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.