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LIT-1881: Bridging Freidlin-Wentzell large deviations theory and stochastic thermodynamics

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Properties5
StatusActive — read in full 2026-10-31 (NOTE-1465); worth reading as the short, self-contained proof, for overdamped diffusions, that a nonequilibrium escape rate e^{−ΩΔI} is bracketed by the entropy produced in relaxing into the attractor and in escaping it (THEORY-1264), with a recursive expansion of the quasi-potential about the free energy. The bracket closes only at detailed balance.
Version2
Tagsthermodynamics, mathematics
Cited as “paper” byNOTE-1465 — Santolin et al. — Freidlin-Wentzell and stochastic thermodynamics
Cited as “source” byTHEORY-1264 — Far from equilibrium, the weak-noise escape rate from an attractor goes as the exponential of minus system size times a barrier in the quasi-potential, not in any free energy, and that barrier is bracketed by thermodynamics: it is at most the entropy produced in relaxing from the saddle into the attractor and at least minus the entropy produced along the most likely escape path; the two bounds coincide at detailed balance and separate by twice the dissipation of the probability circulation, so far from equilibrium they can be very loose

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Santolin, D., Freitas, N., Esposito, M., & Falasco, G. (2025). Bridging Freidlin-Wentzell large deviations theory and stochastic thermodynamics. Physical Review E, 111, 024106.

Read in full in NOTE-1465.

Why this is here

With LIT-1892, A14’s source for reading a maintained regime’s lifetime and escape route thermodynamically, beside the SLT reading of a posterior concentrating on a singular set. The reading supplies the theorem: lifetime e^{ΩΔI}, with ΔI between the dissipation of relaxing in and minus that of escaping out (THEORY-1264). It also marks where the SLT side has no counterpart: the circulation that separates relaxation from escape, and so opens the bracket, is absent from a Gibbs posterior.

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