Extending the mean first-passage-time formalism to the reconstruction of high free-energy barriers: A top-start approach
Abstract
Rare events, such as crystal nucleation in mildly supercooled liquids, are characterized by waiting times that can be much longer than the timescale of the underlying microscopic dynamics. The mean first-passage time (MFPT) formalism [J. Wedekind and D. Reguera, J. Phys. Chem. B 112, 11060 (2008)] provides a route to reconstruct one-dimensional free-energy profiles from the MFPT and steady-state distribution measured along a reaction coordinate, but conventional implementations become inefficient for sufficiently high barriers because spontaneous crossings are rarely observed. We introduce a "top-start" extension that initiates trajectories near the barrier top and reconstructs the free-energy profile from their subsequent evolution away from the barrier toward lower-free-energy regions. We establish the equivalence between the top-start and two-region constructions using a Markov-chain transition-matrix formulation. We validate the method using one-dimensional random-walk simulations across low, medium, and high free-energy barriers, with transition-matrix calculations providing an exact benchmark for the corresponding discretized models. The top-start reconstruction remains accurate in the high-barrier regime where conventional MFPT sampling becomes prohibitively inefficient.
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BibTeX
@misc{jiang2026extending,
title = {{Extending the mean first-passage-time formalism to the reconstruction of high free-energy barriers: A top-start approach}},
author = {Ying Jiang and Ivan Saika-Voivod},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18653},
eprint = {2610.18653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18653},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Extending the mean first-passage-time formalism to the reconstruction of high free-energy barriers: A top-start approach
AU - Ying Jiang
AU - Ivan Saika-Voivod
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18653
UR - https://arxiv.org/abs/2610.18653
AB - Rare events, such as crystal nucleation in mildly supercooled liquids, are characterized by waiting times that can be much longer than the timescale of the underlying microscopic dynamics. The mean first-passage time (MFPT) formalism [J. Wedekind and D. Reguera, J. Phys. Chem. B 112, 11060 (2008)] provides a route to reconstruct one-dimensional free-energy profiles from the MFPT and steady-state distribution measured along a reaction coordinate, but conventional implementations become inefficient for sufficiently high barriers because spontaneous crossings are rarely observed. We introduce a "top-start" extension that initiates trajectories near the barrier top and reconstructs the free-energy profile from their subsequent evolution away from the barrier toward lower-free-energy regions. We establish the equivalence between the top-start and two-region constructions using a Markov-chain transition-matrix formulation. We validate the method using one-dimensional random-walk simulations across low, medium, and high free-energy barriers, with transition-matrix calculations providing an exact benchmark for the corresponding discretized models. The top-start reconstruction remains accurate in the high-barrier regime where conventional MFPT sampling becomes prohibitively inefficient.
ER -