Escape from a fluctuating system: a master equation and trapping approach.

Area of Science:

• Statistical Physics
• Non-equilibrium Systems
• Stochastic Processes

Background:

• Understanding particle or system escape from potential wells is crucial in various scientific fields.
• Previous models often focused on static barriers or specific fluctuation types.
• The phenomenon of resonant activation, where escape rates peak at optimal fluctuation frequencies, requires a general theoretical framework.

Purpose of the Study:

• To develop a general solution for the mean exit time in systems with on-site fluctuations between two configurations.
• To analyze a specific case of coupled birth and death processes exhibiting resonant activation.
• To derive the optimal fluctuating rate analytically and investigate its dependence on system parameters.

Main Methods:

• Formulation of the problem using a master equation describing transitions between two configurations.
• Leveraging general properties of mean exit time to derive a simplified solution.
• Analytical derivation of the optimal fluctuating rate within an exactly solvable model.

Main Results:

• A general solution for mean exit time in fluctuating systems is presented.
• A simple solution for coupled birth-death processes demonstrating resonant activation is obtained.
• The optimal fluctuating rate is derived, shown to be initial-condition dependent and scaling as 1/n with system size n.

Conclusions:

• The developed approach provides a unified framework for various escape problems.
• The findings underscore the general applicability and significance of resonant activation.
• The analytical solution offers precise predictions for systems with fluctuating barriers and modulating channels.