By Ilya Prigogine, Stuart A. Rice
Advances in Chemical Physics, quantity 127 covers fresh advances on the innovative of analysis relative to chemical physics. The sequence, Advances in Chemical Physics, offers a discussion board for serious, authoritative reviews of advances in each quarter of the self-discipline.
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This point is made more explicitly by the hard-sphere data in Table I. One sees that the difference between the values of the free energy  of the two crystalline phases is some four orders of magnitude smaller than the separate results for the two phases, determined by ESM. Of course one can see this as a testimony to the remarkable care with which the most recent recent ESM studies have been carried out . Alternatively, one may see it as a strong indicator that another approach is called for.
32)] and ¼_ means equality to within an overall normalization constant. The procedure by which one uses this equation to estimate the canonical distribution from the measured distribution is variously referred to as ‘‘unfolding the weights’’ or ‘‘re-weighting’’; it is simply one realization of the identity given in Eq. (24). The procedure eliminates any explicit dependence on the weights (hence the looseness of the criteria by which they are speciﬁed), but it leaves the desired legacy: The relative sizes of the two branches of the canonical distribution are determined with a statistical quality that reﬂects the number of interphase traverses in the multicanonical ensemble.
The deﬁning characteristic of an ESPS order parameter is that it measures the difference between the values of some chosen function of the common coordinate set fug evaluated in the two phases, such that for some region (typically ‘‘sufﬁciently small values’’) of that quantity, an interphase switch can be successfully initiated. An ESPS ‘‘order parameter’’ merely provides a convenient thread that can be followed to the wormhole ends. In the case of hard spheres the energy function does not provide a usefully graded measure of how far we are from a wormhole: The order parameter deﬁned in Eq.
Advances in Chemical Physics (Volume 127) by Ilya Prigogine, Stuart A. Rice