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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.