Effective dynamics along given reaction coordinates, and reaction rate theory.

Area of Science:

• Computational chemistry
• Statistical mechanics
• Physical chemistry

Background:

• Molecular dynamics simulates complex systems at atomic detail.
• Reducing complexity involves projecting dynamics onto reaction coordinates.
• Effective dynamics on reaction coordinates are crucial for statistical information.

Purpose of the Study:

• To analyze the properties of effective dynamics induced by full dynamics.
• To derive equations for effective dynamics and assess their accuracy.
• To compare findings with existing methods like Mori-Zwanzig and homogenization.

Main Methods:

• Analysis of ergodic diffusion processes and their invariant measures.
• Derivation of equations governing effective dynamics.
• Comparison with Mori-Zwanzig, averaging, and homogenization techniques.

Main Results:

• Ergodic properties and unique invariant measures are inherited by effective dynamics.
• Effective dynamics provide accurate approximations for timescales and reaction rates.
• Equation-free and heterogeneous multiscale methods are shown as special cases.

Conclusions:

• Effective dynamics accurately capture essential features of full system dynamics.
• The derived framework unifies and extends existing coarse-graining methods.
• This work offers a robust approach for analyzing complex molecular systems.