Entropy Bounds and Capacity-Limited Information Flow in Black-Hole Evaporation

Black-hole evaporation exhibits a range of characteristic entropic phenomena, including Hawking thermality, monotonically increasing radiation entropy in semiclassical treatments, and the Page-curve behavior required by unitarity. These features are accompanied by long-standing puzzles concerning information loss, entanglement growth, and the transfer of correlations between a black hole and its radiation. In this work we present an information-theoretic analysis of these phenomena based on a discrete causal model in which entropy evolution is governed by a competition between the growth of accessible degrees of freedom and a finite capacity for transmitting correlations across a boundary. Radiation is generated through stochastic sampling of interior degrees of freedom, while entanglement between interior and radiation subsystems is constrained by a boundary defined purely at the level of causal connectivity. Within this setting, radiation entropy increases at early times, reaches a maximum when boundary capacity becomes saturated, and decreases thereafter as additional emissions fail to carry independent correlations, yielding Page-curve behavior consistent with unitary evaporation. This capacity-limited mechanism does not rely on semiclassical spacetime geometry or quantum extremal surface constructions and instead follows directly from entropy bounds and information-flow constraints. By isolating the role of finite correlation capacity, the analysis provides a unified entropy-based perspective on black-hole evaporation, complementing semiclassical approaches while remaining applicable in discrete or non-geometric settings.