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Ergodicity of Thermostat Family of Nosé--Hoover type

Hiroshi Watanabe·Hiroto Kobayashi
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Abstract

One-variable thermostats are studied as a generalization of the Nosé--Hoover method which is aimed to achieve Gibbs' canonical distribution with conserving the time-reversibility. A condition for equations of motion for the system with the thermostats is derived in the form of a partial differential equation. Solutions of this equation construct a family of thermostats including the Nosé--Hoover method as the minimal solution. It is shown that the one-variable thermostat coupled with the one-dimensional harmonic oscillator loses its ergodicity with large enough relaxation time. The present result suggests that multi-variable thermostats are required to assure the ergodicity and to work as heatbath.

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Hiroshi Watanabe, Hiroto Kobayashi. 2007-02-09. Ergodicity of Thermostat Family of Nosé--Hoover type. https://doi.org/10.1103/physreve.75.040102

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