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Fluctuation relations for a driven Brownian particle.

A Imparato1, L Peliti

  • 1Dipartimento di Scienze Fisiche, INFN-Sezione di Napoli, CNISM, Sezione di Napoli, Università Federico II, Complesso Monte S. Angelo, I-80126 Naples, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
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We derived a general fluctuation relation for a driven Brownian particle, linking path probabilities to entropy flux. This finding unifies existing fluctuation theorems in statistical mechanics.

Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Brownian Motion

Background:

  • The Kramers equation describes the evolution of probability for a Brownian particle.
  • Understanding path probabilities and their time-reversal is crucial in non-equilibrium systems.
  • Existing fluctuation relations (Seifert, Jarzynski, Gallavotti-Cohen) offer insights into specific scenarios.

Purpose of the Study:

  • To derive a general fluctuation relation for a driven Brownian particle.
  • To express this relation in terms of entropy flux to the heat reservoir.
  • To demonstrate how this general relation encompasses known fluctuation theorems.

Main Methods:

  • Considered a driven Brownian particle subjected to conservative and nonconservative forces.

Related Experiment Videos

  • Utilized the Kramers equation to model the probability evolution.
  • Derived a general fluctuation relation by analyzing Brownian paths in phase space.

    • Main Results:

    • A novel general fluctuation relation was derived for the driven Brownian particle.
    • The relation connects the ratio of forward and time-reversed path probabilities to entropy flux.
    • The derived relation was shown to imply the Seifert, Jarzynski, and Gallavotti-Cohen fluctuation relations under specific conditions.

    Conclusions:

    • The study presents a unified framework for fluctuation relations in non-equilibrium statistical mechanics.
    • The derived relation provides a more general perspective on the thermodynamics of driven Brownian motion.
    • This work contributes to a deeper understanding of the statistical properties of irreversible processes.