Constraints on generalized gravity-thermodynamic cosmology from DESI DR2

We explore the cosmological implications of generalized entropic models within the framework of gravity-thermodynamics (GT) approaches. These models, characterized by three or four additional free parameters, are designed to capture deviations from the standard Bekenstein-Hawking entropy and can reproduce well-known entropic formulations, including Tsallis, Rényi, Sharma-Mittal, Barrow, Kaniadakis, and loop quantum gravity entropies in various analytical limits. We implement the corresponding cosmological models using a fully numerical GT approach to constrain the model parameters and to study the evolution of the dark energy equation of state as a function of the scale factor. Our Bayesian analysis, which incorporates the Pantheon + and DESy5 supernovae data alongside the recently released DESI-DR2/DR1 baryon acoustic oscillation (BAO) measurements, shows that the data favor the standard Bekenstein-Hawking entropy, leading to a Λ CDM -like late-time behavior. In this context, the three-parameter ( S 3 ) entropic model appears to be sufficient to capture the observed dark energy phenomenology. Furthermore, a direct comparison of the Bayesian evidence indicates that the three-parameter model is preferred over the four-parameter ( S 4 ) variant by a factor of Δ log B ∼ − 6 , while the GT approach as a whole is significantly disfavored relative to the Λ CDM model with at least Δ log B ∼ − 8 ( S 3 ) to Δ log B ∼ − 13 ( S 4 ), when using the DESy5 and DESI-DR2 datasets.