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 sector of the self-discipline.
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Extra resources for Advances in Chemical Physics (Volume 127)
First, it is rather more transparent in regard to uncertainties (in free-energy differences). The error bounds emerging from ESIT (and family) represent purely statistical uncertainties associated with the measurement of the relative weights of two distribution-peaks. In contrast, NIRM error bounds have to aggregate the uncertainties (statistical and systematic) associated with different stages of the integration process. Second, it seems rather more satisfying to read-off the result for a free-energy difference directly from the likes of Fig.
Figures 3 and 4 show some explicit results  for a Lennard-Jones ﬂuid. 2. Critique The phase diagram shown in Fig. 4 is of course the ultimate objective of such studies; but it is the distribution shown in Fig. 3 that merits most immediate comment, lest its key feature be taken for-granted. Its ‘‘key feature’’ (which we shall come to recognize as the signature of success in this enterprise) is that it captures the contributions from both phases (the two distinct peaks) within the framework of a single simulation.
The ratio of the two phase probabilities (at a chosen point in ﬁeld space) varies exponentially fast with the system size . Thus for a large system, unless we are very close to coexistence, the equilibrium (grandcanonical) PDF determined in HPT will show signs of only one phase even when there is no ergodic block preventing access to the other phase. If the initial choice is close enough to coexistence to provide at least some signature of the 26 alastair d. bruce and nigel b. wilding subdominant phase , then histogram reweighting techniques (Appendix B) can be used to give a better estimate of coexistence.
Advances in Chemical Physics (Volume 127) by Ilya Prigogine, Stuart A. Rice