Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise
Statistical Mechanics
2026-05-19 v1 Classical Physics
Abstract
Stochastic forces are usually postulated or obtained by eliminating environmental degrees of freedom. Here we identify a variational origin: fluctuating endpoint data in Hamilton's principle induce fluctuations of the on-shell action. Hamilton--Jacobi propagation transports this boundary imprint, whose gradient generates an effective Langevin force inherited from boundary-action fluctuations. The resulting force is not freely specifiable: its amplitude is filtered by the Hessian of Hamilton's principal function, yielding multiplicative and state-dependent noise. Homogeneous additive Langevin forcing is recovered only as a Markovian coarse-grained limit.
Keywords
Cite
@article{arxiv.2605.17621,
title = {Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise},
author = {Francisco Monroy},
journal= {arXiv preprint arXiv:2605.17621},
year = {2026}
}