Properties as Ensemble Averages

Because phase space encompasses every possible state of a system, the average value of a property A at equilibrium (i.e., its expectation value) for a system having a constant temperature, volume, and number of particles can be written as an integral over phase space 

The MC method, described in Section 3.4, is a scheme designed to do exactly this in a pseudo-random fashion. Before we examine that method, however, we first consider a somewhat more intuitive way to sample useful regions of phase space. 

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