Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911692341903360 |
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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 |
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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 |