Volume-Law Entropy as a Mesoscopic Anomaly

Area-law entropy appears in quantum many-body systems and gravitational physics, whereas classical thermodynamics treats entropy as volume-extensive. Rather than reflecting competing fundamental principles, we show that these scalings correspond to distinct thermodynamic stability regimes. Using a minimal information-theoretic free-energy functional combining Fisher information and Shannon entropy, we analyze entropy scaling under three physically unavoidable requirements: locality of response, existence of thermodynamic equilibrium, and universality of gravitational coupling. Within this framework, we prove that volume-law entropy cannot define an intrinsically stable equilibrium for isolated macroscopic systems and is therefore viable only as an externally stabilized, mesoscopic approximation. We identify three regimes. At microscopic scales, Fisher dominance and locality of information propagation enforce area-law entropy. At intermediate scales, volume-law entropy emerges as a metastable regime sustained by non-gravitational confinement. At macroscopic scales dominated by self-gravity, we show that thermodynamic stability and composition-independent equilibrium uniquely require area-law entropy; any more extensive scaling leads either to instability or to violations of the equivalence principle. Volume-law entropy is thus identified as a mesoscopic anomaly rather than a fundamental property of matter. Area-law scaling emerges as the only entropy behavior consistent with a unified thermodynamic description spanning quantum coherence and gravitational universality.