Model-independent reconstruction of cosmic thermodynamics and dark energy dynamics

Abstract

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 reconstructed redshift range, we evaluate key thermodynamic quantities associated with the apparent horizon, including the diagnostic function P ( z ), the entropy production rate

, and its second derivative

$${{\ddot{S}}}_{\textrm{tot}}$$ S ¨ tot

. Within the observationally reconstructed late-time redshift range, we find that P ( z ) remains positive for all dataset combinations, supporting the validity of the generalized second law of thermodynamics. Correspondingly,

$${{\dot{S}}}_{\textrm{tot}} > 0$$ S ˙ tot > 0

throughout, while

$${{\ddot{S}}}_{\textrm{tot}} < 0$$ S ¨ 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 Matérn kernels with

$$\nu = 5/2, 7/2,$$ ν = 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 that the inferred preference for dynamical dark energy is sensitive to both the adopted supernova compilation and the GP kernel, ranging from consistency with

$$\Lambda $$ Λ

CDM to a moderate (

$$\sim 2$$ ∼ 2

–

$$4\sigma $$ 4 σ

) preference for evolving dark energy, with all reconstructions exhibiting a crossing of the

$$w=-1$$ w = - 1

boundary at intermediate redshifts.