We investigate the observational tests of generalized mass-to-horizon entropic cosmology by incorporating large-scale structure growth data in addition to purely geometric probes. The theoretical framework is constructed from a generalized mass-to-horizon scaling relation, $M\propto L^n$, which implies a corresponding generalized entropic functional $S_n\propto L^{n+1}$. Within this setting, cosmic acceleration arises as an emergent phenomenon driven by an entropic force acting on the cosmological horizon. While earlier studies demonstrated that these entropic cosmologies can reproduce the background expansion history of the standard Lambda cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) model, here we present a comprehensive observational analysis that jointly employs $\mathrm{Pantheon}+\text{Type}$ Ia supernova data with SH0ES Calibration, DESI DR2 baryon acoustic oscillation measurements, cosmic microwave background distance priors, and a suite of cosmological structure growth observations. A Bayesian model comparison indicates that the entropic models are statistically preferred over the conventional $\mathrm{\Lambda }\mathrm{CDM}$ scenario, thereby providing strong support for an entropic origin of the observed late-time cosmic acceleration in place of a fundamental cosmological constant.

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• Cosmological parameters
• Dark energy
• Evolution of the Universe
• General relativity