Model-independent reconstruction of cosmic thermodynamics and dark energy dynamics

We perform a model-independent investigation of the thermodynamic evolution of the Universe by reconstructing the expansion history from observational data using Gaussian Process regression. We consider three independent combinations of datasets, namely CC32+DESI DR2+Pantheon+, CC32+DESI DR2+Union3, and CC32+DESI DR2+DES Y5, allowing us to assess the impact of different supernova samples on the reconstruction. From the reconstructed Hubble parameter and its derivatives over the redshift range 0 to 2, we evaluate key thermodynamic quantities associated with the apparent horizon, including the diagnostic function $P(z)$, the entropy production rate $\dot{S}_{\mathrm{tot}}$, and its second derivative $\ddot{S}_{\mathrm{tot}}$. We find that $P(z)$ remains positive across all redshifts, ensuring the validity of the generalized second law of thermodynamics. Correspondingly, $\dot{S}_{\mathrm{tot}} > 0$ throughout, while $\ddot{S}_{\mathrm{tot}} < 0$ at low redshifts, indicating that the Universe evolves toward stable thermodynamic equilibrium. To assess methodological robustness, the reconstruction is performed using multiple covariance kernels, including the Squared Exponential and Mat\'ern kernels with $\nu = 5/2, 7/2,$ and $9/2$, all of which yield consistent results within uncertainties. We also reconstruct the dark energy equation of state in a fully model-independent manner and find it to be consistent with a cosmological constant at the present epoch, with no statistically significant deviation from $\Lambda$CDM.