Volume-Law Entropy as a Mesoscopic Anomaly.

Area-law entropy appears in local quantum ground states, low-temperature Gibbs states, and gravitational physics, whereas classical thermodynamics is formulated with volume-extensive entropy. We propose a coarse-grained information-theoretic framework, based on an effective free-energy functional combining Fisher information, a potential term, and Shannon entropy, that organises these different scalings within a single thermodynamic picture. Comparing localisation costs, external stabilisation, and gravitational self-interaction at the level of scaling reveals three regimes. At microscopic scales, locality and low-temperature coherence enforce area-type entropy scaling. At intermediate scales, volume-law entropy emerges as an effective regime sustained by non-gravitational confinement or external support; in the absence of such support, volume-extensive entropy does not by itself define an intrinsically stable equilibrium. At large scales dominated by gravitational self-interaction, a reduced scaling analysis identifies area-type behaviour as the distinguished infrared scaling, consistent with black-hole thermodynamics and with macroscopic universality requirements. The framework clarifies the limited domain of classical extensivity and offers a unified coarse-grained perspective on the recurrence of area-law scaling across quantum and gravitational settings.