Ergodicity of Thermostat Family of Nosé--Hoover type

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.

4 pages, 2 figures, Submitted to Phys. Rev. E. New results were added

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