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Extended heat-fluctuation theorems for a system with deterministic and stochastic forces.

R van Zon1, E G D Cohen

  • 1The Rockefeller University, 1230 York Avenue, New York, New York 10021, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
Summary

This study explores heat fluctuations in a Brownian particle system, revealing an extended fluctuation theorem that modifies conventional understanding due to deterministic and stochastic motion interactions. The extended theorem shows a significantly higher probability ratio for heat absorption versus supply in large fluctuation events.

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Area of Science:

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

Background:

  • Understanding heat fluctuations is crucial in non-equilibrium systems.
  • Brownian motion in driven potentials presents complex deterministic and stochastic dynamics.
  • Conventional fluctuation theorems provide a baseline for thermodynamic consistency.

Purpose of the Study:

  • To investigate heat fluctuations in a system with both deterministic and stochastic components.
  • To derive and analyze an extended heat fluctuation theorem for such systems.
  • To compare theoretical predictions with numerical and algorithmic results.

Main Methods:

  • Utilizing a Langevin equation to model the Brownian particle's motion.
  • Calculating the exact Fourier transform of heat fluctuation distributions.

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  • Employing a saddle-point method for inverse Fourier transform and analytical results.
  • Validating results with sampling methods and fast Fourier transform algorithms.

    • Main Results:

    • Exact analytical results for heat fluctuation distributions were obtained.
    • The extended fluctuation theorem was derived, differing measurably from the conventional one.
    • Analytical results showed excellent agreement with numerical simulations for larger timescales (tau).
    • A significantly larger ratio of heat absorption to supply probability was observed for large fluctuations.

    Conclusions:

    • The interaction between deterministic and stochastic motion necessitates an extended heat fluctuation theorem.
    • The derived theorem offers a more accurate description of heat fluctuations in this specific non-equilibrium system.
    • The findings have implications for understanding energy transfer in driven soft matter systems.