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.
A central question for the foundations of thermodynamics is which conceptual structures underpin the existence of entropy and temperature. Jauch claimed that entropy and temperature could be derived from a novel conservation law. This paper reconstructs the physics and mathematics of Jauch’s claim and finds that his original proof is not valid. Remarkably, his theorem is still true. We provide an alternative proof using geometric ideas from modern gauge theory, revealing a deep geometric structure in thermodynamics. This result also helps to settle an old debate by showing that entropy and temperature can be defined in a new, conceptually clear way without appeal to an irreversible assumption like the second law.
Decoherence explains why selected quantum histories behave as mutually exclusive alternatives with Born weights, but it does not by itself show that such alternatives are worlds. We formulate this as a geometric representability problem within decoherent histories. A world-bearing branch must support a local physical representation: a compatible spectral and local structure sufficient for spacetime-like observables, stable records, and observer-level description. For a history effect F_α =K_α ^† K_α and a positive spectral probe A , we introduce the branch-resolved heat trace Θ _α (t)=Tr(e^-tA/2F_α e^-tA/2) . Its small-time behavior tests the spectral supply carried by that branch. We prove that identical decoherence data can be realized by branches with inequivalent heat profiles, and that exact decoherent refinement can decompose a spectrally thick branch into probability-bearing but spectrally thin branches. A positive lower-bound theorem then shows that genuine branch-local spectral regularity forces corresponding heat-trace growth. Decoherence remains essential for probabilities, but branch ontology requires structural admissibility beyond decoherence.
