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Fluctuation theorem for a deterministic one-particle system
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
Summary
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:
- 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.