Abstract:Doob fixed-time conditioning enables the sampling of rare trajectories of Markov processes by modifying the drift so that reaching a prescribed target at a given time is guaranteed. We study the statistics of this conditioned path ensemble through the moment generating function in the weak-noise large deviation regime. Since the Doob drift is rarely available in closed form, we reinterpret the conditioned ensemble as the original process post-selected on the terminal constraint, thereby avoiding explicit construction of the Doob transform. This viewpoint then yields an optimal-control representation for the leading exponential contribution to the generating function, expressed as a variational principle with terminal boundary conditions set by the Doob end-point constraint. We illustrate the framework with two analytical examples and with an application to heat dissipation of a minimal model of biomolecular folding.
| Comments: | 13 pages + Appendices, 4 figures |
| Subjects: | Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Probability (math.PR) |
| Cite as: | arXiv:2605.24537 [cond-mat.stat-mech] |
| (or arXiv:2605.24537v1 [cond-mat.stat-mech] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24537 arXiv-issued DOI via DataCite (pending registration) |
From: Francesco Coghi [view email]
[v1]
Sat, 23 May 2026 12:09:23 UTC (2,162 KB)
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