Additive eigenvectors as optimal reaction coordinates, conditioned trajectories, and time-reversible description of...

Area of Science:

• Physical Chemistry
• Computational Chemistry
• Statistical Mechanics

Background:

• Analyzing complex multidimensional stochastic dynamics often involves diffusion on free energy landscapes using reaction coordinates (RCs).
• Optimal RCs are crucial for quantitatively accurate descriptions, with the committor function being a key example for equilibrium dynamics.
• Limitations exist in using the committor function for certain dynamic analyses.

Purpose of the Study:

• To introduce additive eigenvectors (addevs) as optimal reaction coordinates to overcome limitations of the committor function.
• To develop a new theoretical framework for analyzing stochastic dynamics using addevs.
• To provide a time-reversible description of stochastic processes.

Main Methods:

• Derivation of an addev master equation for Markov chains.
• Analysis of stationary and non-stationary solutions of the addev master equation.
• Application of the framework to model systems like unidirectional random walk and diffusion.

Main Results:

• A stationary solution describes sub-ensembles of trajectories with consistent forward and time-reversed dynamics (stochastic eigenmodes).
• Non-stationary solutions describe probability distribution evolution in a time-reversible manner.
• The framework successfully illustrates dynamics on model systems.

Conclusions:

• Additive eigenvectors provide a powerful and versatile tool for analyzing complex stochastic dynamics.
• The addev master equation offers a time-reversible alternative to standard master equations.
• This approach enhances the understanding of trajectory ensembles and system evolution.