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

Francisco Monroy

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arXiv · 2605.17621

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

Francisco Monroy

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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.

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Francisco Monroy. 2026-05-17. Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise. https://arxiv.org/abs/2605.17621

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