Effect of Memory and Active Forces on Transition Path Time Distributions.

Area of Science:

• Statistical mechanics
• Physical chemistry
• Biophysics

Background:

• Understanding transition path times is crucial for analyzing dynamic processes in various scientific fields.
• Stochastic processes, including Markovian and non-Markovian dynamics, are fundamental to modeling these transitions.
• Active forces and memory effects can significantly alter system dynamics.

Purpose of the Study:

• To derive an analytical expression for transition path time distributions for a particle crossing a parabolic barrier.
• To investigate the influence of non-Markovian dynamics (power-law memory) and Markovian dynamics with active forces on these distributions.
• To provide insights for experimental analysis of transition path times in (bio)molecular systems.

Main Methods:

• Derivation of analytical expressions for transition path time distributions.
• Analysis of a generalized Langevin equation with a power-law memory kernel (non-Markovian case).
• Modeling of Markovian processes with noise violating the fluctuation-dissipation theorem to represent active forces.

Main Results:

• Non-Markovian anomalous dynamics impact short-time behavior only for rare events, not overall statistics.
• Long-time decay is consistently exponential, contradicting previous stretched exponential decay suggestions.
• Active forces in Markovian processes decrease the average transition path time without significantly altering short-time behavior.

Conclusions:

• The study provides a theoretical framework for understanding transition path times under non-standard conditions.
• Findings highlight the distinct roles of memory effects and active forces in stochastic dynamics.
• The results offer valuable perspectives for interpreting experimental data in condensed matter and biophysics.