Page-Curve Behavior from Capacity-Limited Information Flow

Abstract We examine how Page-curve behavior can arise in a fully discrete, causal-informational model that does not assume semiclassical geometry, tensor-network structure, chaotic dynamics, or quantum extremal surfaces. The model consists of a network of elementary events connected by directed influence links, with finite-dimensional Hilbert spaces assigned to events and correlations transmitted only along these links. Radiation is produced by stochastic sampling of interior degrees of freedom, while correlations between interior and radiation are constrained by a capacity bound defined purely on the incidence boundary separating the two subsystems. We show that the competition between the linear growth of radiated content and the finite cross-boundary correlation capacity generically produces a Page-like entropy curve. The Page time corresponds to the saturation of this capacity, and the subsequent entropy decrease follows from the rank deficiency of the correlation matrix once no new independent correlations can be transmitted. These results demonstrate that Page-curve behavior can emerge from a minimal structural principle—capacity-limited information flow across a causal boundary—without invoking geometric extremization, minimal-cut arguments, or chaotic operator growth. The analysis provides a fully non-geometric formulation of the informational mechanism underlying unitary evaporation and suggests that geometric representations of the Page curve in holographic and QES frameworks may reflect a deeper, more primitive constraint on correlation flow rather than the fundamental origin of the phenomenon.