Nonreversible Gauge Fields in Fokker–Planck Dynamics: Supersymmetric Hamiltonians and Realized Finite Forces

arXiv:2606.06412v1 Announce Sort: cross
Summary: We formulate stationary-density-preserving nonreversible perturbations of Fokker–Planck dynamics as gauge fields that deform leisure spectra whereas leaving the invariant state fastened. When detailed stability holds, a similarity transformation maps the reversible Fokker–Planck operator to a Witten-Laplacian-type supersymmetric Hamiltonian; nonreversible gauges then seem as non-Hermitian perturbations that protect the zero mode however modify the excited spectrum. This operator viewpoint provides a standard language for leisure gaps, circulating likelihood currents, hypocoercive acceleration, and finite management prices. We signify admissible gauge currents by antisymmetric tensor fields and establish the detailed-balance-violating Ohzeki–Ichiki pressure as a relentless symplectic instance whose infinite-strength restrict is Hamiltonian dynamics. The continual-time spectral hole alone doesn’t choose a finite gauge power, so we introduce a finite-time regularized goal and an actor–critic process for studying the gauge. An precisely solvable anisotropic Gaussian Ornstein–Uhlenbeck benchmark separates the spectral transition from the finite-time optimum and reveals that the discovered gauge recovers the Lyapunov-equation optimum. A double-well benchmark then illustrates the identical constrained choice in a nonconvex metastable panorama. Stochastic gradient strategies enter this framework as bodily related Fokker–Planck programs: mini-batch noise acts as an efficient diffusion tensor, and adaptive strategies akin to Adam correspond to metric selections with doable nonequilibrium currents.



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