Thermodynamic Selection of Reality: Metric Bandwidth, Transport Closure, and the Viability of Histories

Wave-dominated systems admit rich superposed dynamics at the microscopic level, yet observed reality is dominated by a sparse set of effectively classical histories. Explaining this selection without invoking observer-dependent postulates remains a central problem across quantum foundations, semiclassical transport, and nonequilibrium physics. In this work, we establish a rigorous equivalence between two previously independent constraints on history viability: closure preservation in phase-space transport and coherence preservation under a context-induced metric.

We prove that, within a physically relevant class of systems, transport-induced covariance growth and metric-induced distinguishability impose identical bounds on the admissible set of histories. This equivalence reveals history selection as a capacity-limited geometric process: histories persist if and only if their deformation remains within a finite coherence bandwidth. We further show that this bandwidth is not kinematic but must be maintained against transport load by sustained physical flux, giving rise to a natural thermodynamic structure without modifying underlying wave dynamics.

Within this framework, entropy increase corresponds to loss of accessible distinction, the second law emerges as a no-free-bandwidth principle, and equilibrium appears as the zero-flux fixed point. Ontology itself is thereby reinterpreted as a thermodynamic phase: reality consists of those histories that remain dynamically viable under finite energetic support. The results provide a unified, observer-independent account of classicality, irreversibility, and history selection, with experimentally testable implications for coherence control and interference phenomena.