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Anomalous fluctuation properties.

H Touchette1, E G D Cohen

  • 1School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom. ht@maths.qmul.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary
This summary is machine-generated.

This study explores anomalous fluctuation properties in nonequilibrium systems driven by Lévy noise. It reveals distinct behaviors for work and dissipated work distributions based on the noise

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Stochastic Processes

Background:

  • Extends previous research on fluctuations in nonequilibrium steady states driven by Lévy noise.
  • Focuses on systems driven by Lévy noise, a type of stochastic process with heavy tails.

Purpose of the Study:

  • To investigate the probability distributions of work done and work dissipated in a nonequilibrium steady state.
  • To analyze how these distributions behave under different conditions of Lévy noise, specifically the tail index mu.
  • To identify and characterize anomalous fluctuation properties.

Main Methods:

  • Considered a model system: a particle subjected to drag force and Lévy white noise.
  • Calculated the probability distributions for work done and work dissipated.
  • Analyzed these distributions in the context of large deviation theory.

Main Results:

  • For 0 < mu < 2, an anomalous fluctuation property was observed, where positive and negative fluctuations have asymptotically equal probability.
  • For mu = 2, conventional and extended fluctuation relations were recovered, with positive fluctuations being exponentially more probable.
  • Highlighted the distinct fluctuation behaviors based on the Lévy noise tail index.

Conclusions:

  • The study demonstrates a transition in fluctuation behavior in nonequilibrium systems driven by Lévy noise.
  • Anomalous fluctuation properties are characterized by symmetric probability distributions of work fluctuations.
  • Experimental approaches to observe these anomalous fluctuations are proposed.