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Generation of arbitrary probability distributions from chaotic dynamics.

M J Poulos1

  • 1Princeton Plasma Physics Laboratory, 100 Stellarator Road, Princeton, New Jersey 08540, USA.

Physical Review. E
|November 16, 2021
PubMed
Summary

A new framework creates chaotic dynamical systems to generate complex probability distributions using deterministic paths. This extends thermostat methods for advanced physics simulations.

Area of Science:

  • * Physics
  • * Computational Science
  • * Statistical Mechanics

Background:

  • * Traditional dynamical systems often struggle to reproduce complex, arbitrary probability distributions.
  • * Existing thermostat methodologies may have limitations in handling non-Gaussian or anisotropic momentum distributions.

Purpose of the Study:

  • * To develop a general framework for deriving nonlinear dynamical systems capable of generating arbitrary multivariate probability distributions.
  • * To extend the Nosé-Hoover thermostat methodology to more complex scenarios.
  • * To provide pedagogical examples of generating known physical distributions.

Main Methods:

  • * Development of a theoretical framework for constructing nonlinear dynamical systems.
  • * Application of the framework to generalize the Nosé-Hoover thermostat.

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  • * Implementation of toy models to demonstrate the generation of specific probability distributions.

    • Main Results:

    • * A method to derive deterministic chaotic systems for arbitrary probability distributions is established.
    • * The Nosé-Hoover thermostat is successfully extended to three-dimensional, non-Gaussian, and non-isotropic momentum distributions.
    • * Toy models demonstrate the practical generation of various physical distributions.

    Conclusions:

    • * The developed framework offers a powerful tool for creating complex probability distributions from deterministic chaotic systems.
    • * This work advances thermostat methodologies in computational physics, enabling more realistic simulations.
    • * The pedagogical examples facilitate understanding and application of the framework.