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Fluctuation-dissipation relations for Markov processes.

Gregor Diezemann1

  • 1Institut für Physikalische Chemie, Universität Mainz, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
Summary

The fluctuation-dissipation relation in stochastic models is complex. A new "asymmetry" function is needed for stationary processes, impacting glassy relaxation models and effective temperature definitions.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics

Background:

  • The fluctuation-dissipation theorem relates system response to equilibrium fluctuations.
  • Stochastic models described by master equations are crucial for understanding complex systems.

Purpose of the Study:

  • To investigate the fluctuation-dissipation relation for stochastic models with continuous time.
  • To identify and characterize a previously underappreciated asymmetry function in non-equilibrium stationary processes.

Main Methods:

  • Calculation of the fluctuation-dissipation relation for master equations.
  • Analysis of correlation functions and linear response.
  • Investigation of the role of dynamical variables and propagators.

Main Results:

  • A simple fluctuation-dissipation relation does not generally hold for nonstationary processes.
  • For stationary processes, linear response requires an additional "asymmetry" function beyond correlation time-derivatives.
  • This asymmetry depends on the chosen observable and is crucial in glassy relaxation models.

Conclusions:

  • The asymmetry function is essential for understanding fluctuation-dissipation in non-equilibrium systems.
  • Its behavior is strongly dependent on the observable, particularly in systems like trap models.
  • The findings have implications for defining effective temperatures in complex systems.

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