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Direct evaluation of large-deviation functions.

Cristian Giardinà1, Jorge Kurchan, Luca Peliti

  • 1Eurandom, Post Office Box 513 - 5600 MB Eindhoven, The Netherlands.

Physical Review Letters
|April 12, 2006
PubMed
Summary
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We present a new numerical method for efficiently calculating large deviation probabilities of physical quantities. This approach bypasses rare events, enabling wider value ranges and faster computation for systems like the Totally Asymmetric Exclusion Process.

Area of Science:

  • Statistical Physics
  • Computational Physics
  • Non-equilibrium Systems

Background:

  • Calculating probabilities of rare events in physical systems is computationally challenging.
  • Large deviations in quantities like current and density often require extensive simulations.

Purpose of the Study:

  • To introduce a novel numerical procedure for directly evaluating large deviation probabilities.
  • To develop a method that efficiently computes these probabilities over extended ranges.

Main Methods:

  • The proposed method reformulates the problem in terms of a modified dynamical process.
  • It avoids the direct simulation of rare, large-deviation events.
  • The large-deviation functions are derived from the typical properties of this modified dynamics.

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Main Results:

  • The numerical procedure allows for efficient evaluation of large deviation functions.
  • The method is demonstrated to be effective for analyzing current fluctuations in the Totally Asymmetric Exclusion Process.
  • It is also applied to study the work distribution in a driven Lorentz gas.

Conclusions:

  • The new numerical procedure offers an efficient and broadly applicable tool for large deviation studies.
  • It simplifies the computation of rare event probabilities in complex physical systems.
  • This method opens avenues for more extensive investigations into non-equilibrium statistical mechanics.