Energy fluctuations induced by the Nosé thermostat

The Nosé thermostat is a method for simulating a canonical ensemble in molecular-dynamics calculations. It is generally agreed that for large values of Q, the parameter determining the response of the thermostat to the system, the approach to equilibrium is slow and for intermediate values it is rapid. However, for small Q Nosé found the thermostat oscillates rapidly and does not equilibrate with the system; we found it equilibrates but yields incorrect values for energy fluctuations, whereas Cho and Joannopoulos found it equilibrates very slowly, eventually yielding correct energy fluctuations. Here we demonstrate how these differences arise.