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Finite-size fluctuations in interacting particle systems.

E Ben-Naim1, P L Krapivsky

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. ebn@lanl.gov

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 1, 2004
PubMed
Summary

Statistical fluctuations significantly impact interacting particle systems, even at the mean-field level. For a cyclic trapping reaction, the final particle count scales logarithmically with system size due to these fluctuations.

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Area of Science:

  • Statistical physics
  • Chemical kinetics

Background:

  • Interacting particle systems are fundamental in various scientific domains.
  • Mean-field theory often simplifies system dynamics but may overlook crucial fluctuation effects.

Purpose of the Study:

  • To investigate the role of statistical fluctuations in a finite, interacting particle system.
  • To analyze a three-species cyclic trapping reaction model.

Main Methods:

  • Modeling a three-species cyclic trapping reaction with a large, finite number of particles.
  • Analyzing the scaling behavior of the final particle number with system size.

Main Results:

  • The final number of particles, N(f), exhibits a logarithmic dependence on the system size, N (N(f) ≈ ln N).

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  • Statistical fluctuations become significant as particle numbers decrease, driving this scaling behavior.

    • Conclusions:

    • Fluctuations play a critical role in determining the macroscopic behavior of interacting particle systems, even beyond the thermodynamic limit.
    • The observed phenomenon is relevant to other systems, such as multispecies annihilation processes.