Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise

Fuente: arXiv
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Main Author: Monroy, Francisco
Format: Preprint
Published: 2026
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author Monroy, Francisco
author_facet Monroy, Francisco
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_17621
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise
Monroy, Francisco
Statistical Mechanics
Classical Physics
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.
title Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise
topic Statistical Mechanics
Classical Physics
url https://arxiv.org/abs/2605.17621