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Fluctuation theorem for a deterministic one-particle system.

Malte Schmick1, Mario Markus

  • 1Max-Planck-Institut für Molekulare Physiologie, Postfach 500247, 44202 Dortmund, Germany. malte.schmick@mpi.dortmund.mpg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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The fluctuation theorem for a Duffing oscillator is satisfied with just one chaotic time series, challenging previous requirements for many-particle or stochastic systems.

Area of Science:

  • Nonlinear dynamics
  • Statistical mechanics
  • Chaos theory

Background:

  • The fluctuation theorem is a key concept in non-equilibrium statistical mechanics.
  • Previous studies suggested it requires many-particle systems or stochastic processes.

Purpose of the Study:

  • To investigate the minimal conditions for the fluctuation theorem's validity.
  • To analyze the behavior of a Duffing oscillator driven by chaotic time series.

Main Methods:

  • Simulating a Duffing oscillator driven by N chaotic time series.
  • Analyzing the power J(tau) averaged over intervals of length tau.
  • Examining the probability distributions p(J(tau)) and the relationship ln[p(J(tau))/p(-J(tau))] versus J(tau).

Main Results:

Related Experiment Videos

  • N=1 chaotic time series is sufficient to satisfy the fluctuation theorem.
  • The probabilities p(J(tau)) exhibit a near-Gaussian distribution.
  • The function ln[p(J(tau))/p(-J(tau))] shows a linear dependence on J(tau) for large tau, with slopes proportional to tau.

Conclusions:

  • The fluctuation theorem can be valid without many-particle systems or stochastic processes.
  • A single chaotic driver is sufficient for a Duffing oscillator to exhibit fluctuation theorem properties.