Entropic Chaplygin-Gas cosmology and late-universe tension diagnostics

Persistent discrepancies between early- and late-Universe measurements have made cosmological tensions a major test of the standard $\Lambda$CDM model. We investigate whether an entropic generalized Chaplygin-gas cosmology, describing a unified dark sector, can modify the parameter degeneracies associated with these tensions. The model is constrained using Type Ia supernova data from PantheonPlus+SH0ES and DES--Dovekie, DESI BAO measurements, RSD growth data, compressed Planck 2018 distance priors, and a Planck lensing-amplitude prior. We find that the entropic gCg model closely reproduces the $\Lambda$CDM background expansion while introducing a controlled late-time deformation of the distance--redshift relation. This shifts the preferred $(H_0,\Omega_m,S_8)$ region and partially reduces background-driven discrepancies, especially those involving $H_0$. Using \texttt{Tensiometer} to quantify posterior shifts in the common derived parameter space $(H_0,\Omega_m,S_8)$, we show that the displacement relative to $\Lambda$CDM occurs mainly along background-sensitive directions. The model therefore modifies the late-time expansion sector more effectively than the growth sector, leaving residual $S_8$ discrepancies comparatively robust. These results support the possibility that the $H_0$ and $S_8$ tensions arise from distinct physical sectors.