Thermodynamic Averages

To average over a thermodynamic quantity it suffices to average over the values for the sequence of states generated by the Metropolis algorithm. However it is usually wise to carry out a number of Monte-Carlo steps before starting to do any averaging. This is to guarantee that the system is in thermodynamic equilibrium while the averaging is carried out.

The sequence of random changes is often considered as a sort of time axis. In practice we think (e.g. ) about the time required to reach equilibrium. Sometimes, however, the transition rate becomes very low and the system effectively gets stuck in a non-equilibrium state. This is often the case at low temperatures when almost every change causes an increase in energy.