Mass-to-Horizon relation and entropy beyond the Bekenstein-Hawking limit

We introduce a generalized mass–horizon relation applicable to cosmological horizons. This formulation provides a unified framework for deriving a broad class of Bekenstein entropy extensions motivated by statistical mechanics, quantum gravity, and phenomenological considerations, through the application of the Clausius relation together with the Hawking temperature. We further introduce this notion as a foundational framework for constructing generalized entropy forms that remain consistent with thermodynamic laws and the holographic principle.