Quasi-ergodic hypothesis

The quasi-ergodic hypothesis asserts the equivalence of the MD time average (9) with an ensemble average in an ensemble characterized by the constants of the dynamical motion, viz., the volume V, the number of particles N, and at least for most numerical applications, the energy (For an up-... 

As noted in Section 2, the molecular dynamics ensemble is characterized by fixed values of N, V, E and M. All states consistent with these values are equiprobable. According to the quasi-ergodic hypothesis, the trajectory x (t) starting from x should, except possibly for a set of initial phases of zero... 

By the quasi-ergodic hypothesis we replace (W nvem by W and determine the dependence of W on H and M as follows. From the conservation of momentum, one has... 

It should be noted that the pressure determined from (42) becomes identical with the strictly dynamical pressure (29) or (35) only through the application of the quasi-ergodic hypothesis in proceeding from (41) to (42). 

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