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Fluctuation-dissipation relations in driven dissipative systems.

Yair Shokef1, Guy Bunin, Dov Levine

  • 1Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 23, 2006
PubMed
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Time-dependent fluctuation-dissipation relations in driven systems are violated. The fluctuation temperature, derived from correlation-to-response ratios, is shown to depend on measurement time, differing from environmental or granular temperatures.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Non-equilibrium Thermodynamics

Background:

  • Driven dissipative systems are crucial in statistical mechanics.
  • Fluctuation-dissipation relations (FDRs) typically hold in equilibrium systems.
  • Understanding non-equilibrium FDRs is key to characterizing complex systems.

Purpose of the Study:

  • To present exact theoretical results for the violation of time-dependent FDRs.
  • To analyze the measurement time dependence of fluctuation temperature.
  • To investigate the relationship between fluctuation temperature and other system temperatures.

Main Methods:

  • Utilizing a stochastic model previously introduced in Phys. Rev. Lett. 93, 240601 (2004).
  • Calculating the ratio of correlation to delayed response.

Related Experiment Videos

  • Defining and analyzing a fluctuation temperature based on this ratio.

    • Main Results:

    • The ratio of correlation to delayed response depends on measurement time.
    • The defined fluctuation temperature differs from the environment's temperature.
    • The fluctuation temperature is distinct from effective temperatures like granular temperature.
    • Explanations for time independence of fluctuation temperature under specific conditions are provided.

    Conclusions:

    • Time-dependent FDRs are violated in driven dissipative systems.
    • Fluctuation temperature is a time-dependent quantity in these systems.
    • This work provides a theoretical framework for understanding non-equilibrium thermodynamics.