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, presents a discussion board for serious, authoritative reviews of advances in each zone of the self-discipline.
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5 . Here it seems to us that ESIT wins in two respects. 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.
Equation (32) shows how. We need to build a sampling distribution that extends along the path of M-macrostates running between the two phases. C) assign roughly equal values to the probabilities of the different macrostates. More explicitly, the resulting measured distribution of M-values (following Ref. 27 we shall call it multicanonical) PS ðMj Þ ðY dqi PS ðfqgÞÁj ½MðfqgÞ ð42Þ i should be roughly ﬂat. It needs to be ‘‘roughly ﬂat’’ because the macrostate of lowest probability sets the size of the bottleneck through which interphase computational strategies for mapping equilibrium phase diagrams 27 traverses must pass.
Nor do we need these constants in implementing parallel sampling [Eq. (26)] since in this case they feature (through their product) only in the one overall normalization constant for the sampling distribution. But Eq. (28) is different. Writing it out more explicitly, PS ðfqgÞ ¼ W0 X wj eÀEðfqg; Cj Þ ð30Þ j¼1 we see that the weights fwg control the relative contributions that the macrostates make to the sampling distribution. While we are, in principle, at liberty to choose whatever mixture we please [we do not have to make the assignment prescribed by Eq.