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Work-probability distribution in systems driven out of equilibrium.

A Imparato1, L Peliti

  • 1Dipartimento di Scienze Fisiche and Unità INFM, Università Federico II, Associati INFN, Sezione di Napoli, Complesso Monte S. Angelo, I-80126 Napoli, Italy. imparato@na.infn.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
Summary

This study details the differential equation for work probability distribution in non-equilibrium stochastic systems. It shows work distribution is a path integral, dominated by classical paths for large systems, and discusses Jarzynski equality applicability.

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Area of Science:

  • Statistical physics
  • Non-equilibrium thermodynamics
  • Stochastic processes

Background:

  • Understanding the behavior of stochastic systems driven out of equilibrium is crucial in statistical physics.
  • The work probability distribution function (WPDF) provides insights into energy exchange during these processes.
  • The Jarzynski equality offers a method to calculate free energy from non-equilibrium work measurements.

Purpose of the Study:

  • To derive the differential equation governing the time evolution of the WPDF for systems perturbed out of equilibrium.
  • To explore the representation of WPDF using path integrals and analyze its behavior in the large system size limit.
  • To assess the applicability of the Jarzynski equality for free energy calculations in such systems.

Main Methods:

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  • Derivation of a differential equation for the WPDF.
  • Representation of the WPDF using path integrals.
  • Analysis of "classical" paths dominating the path integral in the large system size limit.
  • Comparison with simulated manipulation of mean-field systems.

Main Results:

  • A differential equation for the WPDF of non-equilibrium stochastic systems is derived.
  • The WPDF is shown to be representable by a path integral.
  • In the large system size limit, the path integral is dominated by "classical" paths.
  • Simulations of mean-field systems corroborate the theoretical findings.

Conclusions:

  • The derived framework accurately describes the work probability distribution evolution.
  • The study clarifies the role of "classical" paths in path integral representations of work.
  • Insights into the range of applicability of the Jarzynski equality for free energy calculations are provided.
  • The behavior of large work fluctuations and distribution tails is discussed.