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Computation of large deviation statistics via iterative measurement-and-feedback procedure
Takahiro Nemoto1, Shin-ichi Sasa1
1Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
Physical Review Letters
|March 25, 2014
Summary
We developed a computational method for analyzing rare events in Markov processes. This technique uses feedback-controlled forces to make unusual system behaviors appear typical, aiding statistical analysis.
Area of Science:
- Computational physics
- Statistical mechanics
- Non-equilibrium thermodynamics
Background:
- Analyzing rare events in complex systems is challenging.
- Markov processes are fundamental to modeling dynamic systems.
- Large deviation statistics quantify the probability of rare events.
Purpose of the Study:
- To develop a novel computational method for large deviation statistics.
- To analyze time-averaged quantities in general Markov processes.
- To demonstrate the method's utility in statistical physics models.
Main Methods:
- A feedback-controlled measurement approach is proposed.
- External forces are adjusted based on previous measurements.
- This generates stationary states from an exponential family of distributions.
Main Results:
- The method transforms rare events into typical behaviors.
- It provides a framework for studying large deviations.
- Applied to one-dimensional lattice gas models.
Conclusions:
- The proposed computational method offers a new perspective on large deviation statistics.
- It simplifies the analysis of rare events in Markov processes.
- Applicable to various complex systems in physics and beyond.
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