dorsal/arxiv
View SchemaA theory of state-to-state transitions based on the framework of classical reaction dynamics
| Authors | Kento Kasahara, Ryo Okabe, Chia-en A. Chang, Toshifumi mori, Nobuyuki Matubayasi |
|---|---|
| Categories | |
| ArXiv ID | 2601.09187vv2 |
| URL | https://arxiv.org/abs/2601.09187 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We propose a new method to describe the population dynamics of distinct configurational states based on a continuous-time description of state-to-state transitions. According to classical reaction dynamics theory, the probability density associated with a given state obeys the Liouville equation, the probability density associate d with a given state obeys the Li ouville equation, including influx from and efflux to neighboring states. By introducing a Markov approximation for the crossing of boundaries separating the states, tractable integral equations governing the state populations are derived. Once the time-dependent quantities appearing in these equations are evaluated, the population dynamics on long timescales can be obtained. Because these quantities depend only on a few states in the local neighborhood of a given state, they can be computed using a set of short-timescale molecular dynamics (MD) simulations. We apply the present method to the binding and unbinding kinetics of CH$_4$/CH$_4$, Na$^+$/Cl$^-$, and 18-crown-6-ether (crown ether)/K$^+$ in water. For both kinetics, the time constants estimated from the present method are almost comparable to those obtained from brute-force MD simulations. The required timescale of each MD trajectory in the present method is approximately two orders of magnitude shorter than that in the brute-force MD approach in the crown ether/K$^+$ system. This reduction in the trajectory timescale enables applications to complex binding and unbinding sy stems whose characteristic timescales a re far beyond those directly acce ssible by brute-force MD simulati ons.
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"abstract": "We propose a new method to describe the population dynamics of distinct configurational states based on a continuous-time description of state-to-state transitions. According to classical reaction dynamics theory, the probability density associated with a given state obeys the Liouville equation, the probability density associate d with a given state obeys the Li ouville equation, including influx from and efflux to neighboring states. By introducing a Markov approximation for the crossing of boundaries separating the states, tractable integral equations governing the state populations are derived. Once the time-dependent quantities appearing in these equations are evaluated, the population dynamics on long timescales can be obtained. Because these quantities depend only on a few states in the local neighborhood of a given state, they can be computed using a set of short-timescale molecular dynamics (MD) simulations. We apply the present method to the binding and unbinding kinetics of CH$_4$/CH$_4$, Na$^+$/Cl$^-$, and 18-crown-6-ether (crown ether)/K$^+$ in water. For both kinetics, the time constants estimated from the present method are almost comparable to those obtained from brute-force MD simulations. The required timescale of each MD trajectory in the present method is approximately two orders of magnitude shorter than that in the brute-force MD approach in the crown ether/K$^+$ system. This reduction in the trajectory timescale enables applications to\n complex binding and unbinding sy stems whose characteristic timescales a re far beyond those directly acce ssible by brute-force MD simulati ons.",
"arxiv_id": "2601.09187",
"authors": [
"Kento Kasahara",
"Ryo Okabe",
"Chia-en A. Chang",
"Toshifumi mori",
"Nobuyuki Matubayasi"
],
"categories": [
"physics.chem-ph",
"cond-mat.stat-mech"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "A theory of state-to-state transitions based on the framework of classical reaction dynamics",
"url": "https://arxiv.org/abs/2601.09187",
"version": "v2"
},
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"variant": "snapshot-2026-01-17",
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