Conditional Residence Times and Sequential Transition Dynamics of an Overdamped Dimer

Dhruv Agrawal; W. L. Reenbohn

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arXiv · 2607.06110

Conditional Residence Times and Sequential Transition Dynamics of an Overdamped Dimer

Dhruv Agrawal·W. L. Reenbohn

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Abstract

We investigate the completion dynamics of an overdamped dimer moving in a bistable potential under thermal fluctuations and a weak periodic force. Both monomers start in one of the two wells separated by a barrier. The transition is initiated when the monomer closer to the barrier makes a jump across it. The completion dynamics refers to the next part of the dynamics where the second monomer has to wait for some time before it can follow up. We use the Conditional Residence Time (CRT) to study the delay between the successive barrier crossing of the two monomers. The CRT distributions highlight qualitatively different regimes formed by the competition between the escape times of the lagging monomer and the time period of the external drive. The effect is strongest in the weak coupling regime where the delayed completion is spread across multiple forcing cycles. By partitioning this process into three windows, i.e. the immediate, first cycle and later cycles, we show that the probability that the lagging monomer will make a transition in the said cycle is redistributed among these pathways as we change the frequency of the drive. This leads to a non-monotonic dependence of the mean CRT on the frequency of the drive. Our results demonstrate that transition initiation and completion in a coupled system are two separate processes and establish CRT as a useful measure to quantify the sequential barrier crossing dynamics in coupled stochastic systems.

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Dhruv Agrawal, W. L. Reenbohn. 2026-07-07. Conditional Residence Times and Sequential Transition Dynamics of an Overdamped Dimer. https://arxiv.org/abs/2607.06110

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