Equilibration and Statistical Averaging

A thermodynamically stable system conserves energy. Thus, by monitoring the potential energy one can confirm that a stable (and productive) phase of the simulation has begun. Absence of systematic drift in computed averages is often used as a check on the stability of a Monte Carlo trajectory. Fluctuations in the energy 

For a simulation of finite duration this equality will not 

Averaging and storage of data for a Monte Carlo run are carried out in much the same way as for molecular dynamics (see p. 318-324). 

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