Nosé-Hoover Thermostats: Equations and Time Averages

This lecture by the instructor covers the Nosé-Hoover thermostats, focusing on the real vs virtual variables and the equations associated with the thermostat. It delves into the scaling of momenta through time, time averages in real time, and the transformation of time averages calculated over real time steps. The lecture also discusses the partition function of the Nosé system and the equations of motion in virtual Nosé variables. Additionally, it explores the change of variables, setting the inertia parameter Q, and the distribution of velocities for various Q values. Conclusive remarks highlight the importance of uniform sampling in real time and the limitations of the method in obtaining time-correlations.