Equilibrium principles across physics—Born’s rule, the second law, and Einstein’s curvature–matter balance—are typically assumed rather than derived. We propose the Deterministic Statistical Feedback Law (DSFL), which treats the mismatch between statistical structure and physical response as a Lyapunov-type residual that decays monotonically, often exponentially. In this view, equilibria are dynamical attractors, not postulates. We prove a single template—propagation plus a spectral gap or coercivity—that yields context-dependent rates across five sectors: reversible quantum Markov semigroups (where DSFL is equivalent to a noncommutative Poincaré inequality with optimal rate), finite-dimensional Lindblad dephasing (sharp decay set by the slowest dephasing pair), coercive PDE flows (via an exact residual energy identity), free-field stochastic quantization (decay controlled by the Hamiltonian gap), and geometric DeTurck slices (exponential suppression governed by a Lichnerowicz-type gap). A pointer-algebra perspective shows the law’s form is universal while the attractor and rate are contextual. We also introduce a residual-entropy proxy that increases strictly along DSFL trajectories, providing a structural arrow of time. The framework leads to testable signatures, including coherence bandwidths in gravitational-wave data, phase statistics at low multipoles in the cosmic microwave background, large-scale growth constraints in cosmology, and convergence rates in quantum-optics experiments.
Camilla Josephson (Mon,) studied this question.