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Dichotomous flow with thermal diffusion and stochastic resetting.

Karol Capała1, Bartłomiej Dybiec1, Ewa Gudowska-Nowak1

  • 1Department of Statistical Physics, Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland.

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Summary

Stochastic resonant activation (SRA) and stochastic resetting optimize noise-induced escape through different mechanisms. Resetting eliminates suboptimal paths, while SRA matches dynamic timescales, showing limited synergy in symmetric systems.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Stochastic resonant activation (SRA) and stochastic resetting are phenomena that can optimize noise-induced escape.
  • Both effects share similarities in their ability to enhance system dynamics but possess distinct underlying mechanisms.
  • Understanding their interplay is crucial for controlling stochastic processes.

Purpose of the Study:

  • To investigate the combined effects of SRA and random resetting on one-dimensional diffusive dichotomous flow.
  • To elucidate the differing origins of optimization provided by SRA and stochastic resetting.
  • To determine if stochastic resetting can further enhance SRA in symmetric systems.

Main Methods:

  • Analysis of one-dimensional diffusive dichotomous flow models.
  • Examination of asymptotic properties to distinguish the effects of SRA and stochastic resetting.
  • Comparative study of optimization efficiencies under combined and individual mechanisms.

Main Results:

  • Stochastic resetting optimizes escape by eliminating suboptimal trajectories.
  • SRA optimizes escape by matching timescales within a dynamic environment.
  • Stochastic resetting does not significantly enhance SRA in symmetric setups.
  • The origins of optimization for SRA and stochastic resetting are fundamentally different.

Conclusions:

  • SRA and stochastic resetting offer distinct pathways for optimizing noise-induced escape.
  • The effectiveness of stochastic resetting is tied to trajectory selection, whereas SRA depends on temporal dynamics.
  • Synergistic benefits from combining SRA and stochastic resetting are limited, particularly in symmetric systems.