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

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.