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Tsallis dynamics using the Nosé-Hoover approach.
1National Institute of Advanced Industrial Science and Technology, 2-41-6, Aomi, Koto-ku, Tokyo 135-0064, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
Summary
Researchers developed a deterministic algorithm using the Nosé-Hoover method to generate arbitrary probability densities, including the Tsallis distribution for physical systems in heat baths.
Area of Science:
- Computational Physics
- Statistical Mechanics
Background:
- The Nosé-Hoover method is a common technique for simulating systems in contact with a heat bath.
- The Tsallis distribution is a generalized statistical distribution proposed as a candidate for describing physical systems under non-extensive conditions.
Purpose of the Study:
- To develop a deterministic algorithm capable of producing arbitrary probability densities.
- To implement the Tsallis distribution within a computational framework.
Main Methods:
- Development of a deterministic algorithm based on the Nosé-Hoover method.
- Utilizing an ordinary differential equation to realize the Tsallis distribution density.
- Defining the Tsallis distribution using a full energy function E(x,p) and the Tsallis index q (q >= 1).
Main Results:
- The developed algorithm successfully produces arbitrary probability densities.
- Numerical simulations confirmed the observation of Tsallis distributions for simple systems.
- The ordinary differential equation within the algorithm effectively realizes the Tsallis distribution.
Conclusions:
- The novel deterministic algorithm provides a method for generating Tsallis distributions.
- This approach offers a computational tool for studying physical systems potentially described by Tsallis statistics.