Thermodynamics of sign-switching dark energy models

We perform a comprehensive thermodynamic analysis of three sign-switching dark energy models in a flat FLRW cosmology: graduated dark energy (gDE), sign-switching cosmological constant ($\Lambda_s$), and smoothed sign-switching cosmological constant ($\Lambda_t$). We systematically derive key cosmological thermodynamic quantities -- horizon temperature, horizon entropy, internal entropy, total entropy, and their first and second derivatives -- using the Generalised Second Law (GSL) as the fundamental evaluation criterion. We first confirm the compliance of the $\Lambda$CDM model with the GSL, establishing a baseline for comparison. We find that despite their unconventional negative-to-positive energy density transitions, both $\Lambda_s$ and $\Lambda_t$ remain thermodynamically consistent. In contrast, gDE exhibits significant issues: divergences in its equation-of-state lead to infinite horizon temperature and entropy derivatives; and asymptotically, the horizon temperature diverges while entropy approaches zero, causing entropy reduction and violating the GSL. We highlight a key insight: models with divergences in the product of the dark energy equation-of-state parameter and its energy density ($w_x \Omega_x$) inevitably produce thermodynamic inconsistencies in standard cosmology. This thermodynamic approach provides a complementary criterion alongside observational constraints for evaluating the physical viability of cosmological models.