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Effective stochastic generators for conditioned dynamics at an atypical reaction-diffusion current.

Pegah Torkaman1, Farhad H Jafarpour1

  • 1Physics Department, Bu-Ali Sina University, 65174-4161 Hamedan, Iran.

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Summary
This summary is machine-generated.

This study investigates how to make unusual particle current fluctuations typical in stochastic processes. It identifies conditions where an effective process mirrors the original dynamics, applicable to various time-integrated observables.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Stochastic Processes

Background:

  • Studying fluctuations in particle currents is crucial for understanding non-equilibrium systems.
  • Atypical fluctuations in stochastic Markov processes present unique theoretical challenges.

Purpose of the Study:

  • To determine the necessary interactions to transform atypical particle current fluctuations into typical ones.
  • To explore the conditions under which an effective stochastic process can replicate the dynamics of the original system.

Main Methods:

  • Analysis of a generic stochastic Markov process with two-site interaction and hard-core repulsion on a finite 1D lattice.
  • Investigation of effective stochastic processes with potentially nonlocal transition rates.
  • Identification of conditions for equivalence between the stochastic generators of the original and effective processes.

Main Results:

  • Conditions were found where the effective process's dynamical rules match the original process.
  • The study demonstrates that atypical current values can be made typical by imposing specific interactions.
  • The developed approach is generalizable to other time-integrated observables.

Conclusions:

  • Specific interactions can effectively 'normalize' atypical fluctuations in particle currents within stochastic systems.
  • The equivalence of dynamical rules between original and effective processes simplifies the analysis of non-equilibrium phenomena.
  • This work provides a framework for analyzing fluctuations in a broader range of time-integrated observables in statistical physics.