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Work Fluctuations and Jarzynski Equality in Stochastic Resetting.

Deepak Gupta1, Carlos A Plata1, Arnab Pal2,3,4

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Stochastic resetting of Brownian particles in modulated potential wells leads to universal work fluctuations. The Jarzynski equality is violated for finite times but holds when protocols are not reset.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Soft Matter Physics

Background:

  • Brownian motion describes particle diffusion in a fluid.
  • Stochastic resetting introduces intermittent jumps to a preferred location.
  • Work fluctuations in driven systems are key to understanding non-equilibrium processes.

Purpose of the Study:

  • Investigate work fluctuations in an overdamped Brownian particle system with stochastic resetting.
  • Analyze the convergence of work distribution functions under modulated potentials.
  • Examine the validity of the Jarzynski equality in resetting systems.

Main Methods:

  • Theoretical analysis of an overdamped Brownian particle model.
  • Inclusion of stochastic resetting and modulated potential protocols.
  • Derivation of work distribution functions and comparison with theoretical equalities.
  • Exact solutions and numerical simulations for validation.

Main Results:

  • Work distribution converges to a universal Gaussian form at asymptotic times for renewed protocols.
  • Jarzynski equality is generally not obeyed for finite observation times with resetting.
  • The Jarzynski equality is always satisfied when protocols evolve without resetting.
  • Identified specific protocols that satisfy the Jarzynski equality even with resetting.

Conclusions:

  • Stochastic resetting significantly alters work fluctuation statistics in driven systems.
  • The Jarzynski equality's applicability is restricted in resetting scenarios.
  • Findings provide insights into non-equilibrium thermodynamics and potential experimental realizations.