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Illuminating non-equilibrium multi-step reaction dynamics with stochastic Marcus state model.

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This study introduces a novel stochastic Marcus state model to analyze complex, multi-step chemical reactions. The model clarifies stochastic reaction dynamics and extends Marcus theory to continuous chemical-state spaces.

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Area of Science:

  • Chemical Physics
  • Statistical Mechanics
  • Theoretical Chemistry

Background:

  • Stochastic reaction dynamics are crucial for understanding non-equilibrium processes at mesoscopic scales.
  • Marcus's transition-state theory effectively describes single-step reactions but has limitations for multi-step processes in continuous chemical-state spaces.

Purpose of the Study:

  • To develop a generalized stochastic Marcus state model applicable to multi-step reaction systems.
  • To extend the applicability of Marcus theory to continuous chemical-state spaces.

Main Methods:

  • Development of a stochastic Marcus state model using continuation methods.
  • Employing Fokker-Planck equations to describe the time-resolved evolution of probability density functions.
  • Determining drift and diffusion coefficients from free-energy functions and reorganization energy.

Main Results:

  • The model successfully describes time-resolved probability density functions via Fokker-Planck equations.
  • A scale-invariant transform was identified for systems with infinitesimal-reaction transitions, preserving the model's generic form.
  • The over-damped Langevin dynamics in the chemical-state space were shown to follow the fluctuation-dissipation theorem.

Conclusions:

  • The developed stochastic Marcus state model provides a framework for analyzing multi-step stochastic reaction dynamics.
  • The study demonstrates the generality of the model in classical closed near-equilibrium systems, retrieving the Onsager reciprocal relation under specific conditions.