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A modified set of equations is given for the simulation of a canonical ensemble based on the method introduced by Nos\'e. The equations produce trajectories that are sufficiently chaotic to calculate average properties of a canonical ensemble, even for a small number of degrees of freedom. This important fact is demonstrated by presenting results for a single one-dimensional harmonic oscillator. It is shown that the extended system is chaotic and that the trajectories cover the whole energy surface in phase space.
Roland G. Winkler (1992) studied this question.