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Fluctuation-dissipation relationship in chaotic dynamics

Bag1, Ray

  • 1Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700032, India.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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Researchers explored chaotic systems and found a new relationship between drift and diffusion coefficients, mirroring concepts from nonequilibrium statistical mechanics. This finding, validated in a driven double-well system, offers insights into complex dynamical systems.

Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Dynamics and Chaos Theory
  • Statistical Mechanics

Background:

  • Dissipative systems with N degrees of freedom can exhibit complex chaotic behavior.
  • Understanding the steady-state properties of such systems is crucial for characterizing their dynamics.
  • The fluctuation-dissipation relation is a key concept in nonequilibrium statistical mechanics, linking microscopic fluctuations to macroscopic dissipation.

Purpose of the Study:

  • To establish a relationship between drift and diffusion coefficients in general N-degree-of-freedom dissipative chaotic systems.
  • To demonstrate that this relationship can be expressed using stochastic parameters characterizing the system's steady state.
  • To verify the proposed relationship by comparing it with the established fluctuation-dissipation relation in a relevant physical system.

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Main Methods:

  • Utilized a Fokker-Planck description to model the dynamics of the dissipative chaotic system.
  • Derived a relationship connecting drift and diffusion coefficients via stochastic parameters of the steady state.
  • Employed numerical experiments on a driven double-well system to validate the theoretical findings.

Main Results:

  • A novel relationship was established between drift and diffusion coefficients in dissipative chaotic systems.
  • This relationship is analogous to the fluctuation-dissipation relation found in nonequilibrium statistical mechanics.
  • Numerical simulations on a driven double-well system confirmed the validity of the derived relationship.

Conclusions:

  • The study successfully generalized the concept of fluctuation-dissipation relations to a broader class of dissipative chaotic systems.
  • The findings provide a new theoretical framework for analyzing the steady-state properties of complex dynamical systems.
  • This work bridges concepts from nonlinear dynamics and statistical mechanics, offering potential applications in various scientific fields.