Across physics, core equilibrium relations—Born’s rule, entropy increase, and the curvature–matter balance—are usually postulates, not outcomes. We introduce a single restoration mechanism, the Deterministic Statistical Feedback Law (DSFL), which tracks a quadratic mismatch between a statistical blueprint and a physical response and proves it is a Lyapunov functional. Under standard reversibility or coercivity assumptions, this residual decays exponentially at an explicit, sector-dependent rate set by a spectral gap or a coercivity constant. As a flagship illustration, we restate the classical equivalence between exponential variance decay and a noncommutative Poincaré (spectral-gap) inequality for reversible quantum Markov semigroups, making the rate bookkeeping explicit. We also present two sharp demonstrators: finite-dimensional pure-dephasing Lindbladians, where the envelope is fixed by the slowest dephasing pair, and a coercive PDE template with an exact residual energy identity and a clean exponential envelope. The framework places classical, quantum, and PDE or field examples on the same Lyapunov footing and makes their rates directly comparable across sectors.
Camilla Josephson (Tue,) studied this question.