Ergodicity of a singly-thermostated harmonic oscillator

• Ergodicity has been achieved for a harmonic oscillator
• Only a single thermostat variable is necessary for ergodicity
• The thermostat variable controls both potential and kinetic moments
• A purely kinetic approach can be found in Reference 21
• Both equilibrium and nonequilibrium applications are included

Although Nosé’s thermostated mechanics is formally consistent with Gibbs’ canonical ensemble, the thermostated Nosé–Hoover (harmonic) oscillator, with its mean kinetic temperature controlled, is far from ergodic. Much of its phase space is occupied by regular conservative tori. Oscillator ergodicity has previously been achieved by controlling two oscillator moments with two thermostat variables. Here we use computerized searches in conjunction with visualization to find singly-thermostated motion equations for the oscillator which are consistent with Gibbs’ canonical distribution. Such models are the simplest able to bridge the gap between Gibbs’ statistical ensembles and Newtonian single-particle dynamics.