Accelerated First-Passage Dynamics in a Non-Markovian Feedback Ornstein-Uhlenbeck Process

Area of Science:

• Statistical Physics
• Non-Markovian Dynamics
• Stochastic Processes

Background:

• First-passage time dynamics are crucial in various scientific fields.
• Non-Markovian processes introduce memory effects, complicating traditional analyses.
• Time-averaged feedback mechanisms are increasingly relevant in complex systems.

Purpose of the Study:

• To investigate the impact of time-averaged feedback on non-Markovian stochastic processes.
• To model this system as a one-dimensional Ornstein-Uhlenbeck process with trajectory-dependent drift.
• To analyze the resulting self-interacting diffusion and its first-passage properties.

Main Methods:

• Application of weak-noise large deviation theory.
• Calculation of asymptotic distributions and most probable paths.
• Derivation of the feedback-modified Kramers rate and analysis of mean first-passage time.

Main Results:

• The feedback mechanism accelerates dynamics by storing fluctuations and reducing the effective energy barrier.
• The optimal first-passage time shifts from infinite to finite due to feedback.
• Alternative trajectory mechanisms like slingshot and ballistic paths were found to be sub-optimal.

Conclusions:

• Memory feedback significantly reshapes rare event statistics in stochastic processes.
• This study provides a mechanism for potentially controlling first-passage dynamics.
• The findings offer insights into self-interacting diffusions and their behavior.