By Ilya Prigogine, Stuart A. Rice
Advances in Chemical Physics, quantity 127 covers contemporary advances on the leading edge of study relative to chemical physics. The sequence, Advances in Chemical Physics, presents a discussion board for severe, authoritative reviews of advances in each quarter of the self-discipline.
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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 quarter of the self-discipline.
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Extra info for Advances in Chemical Physics (Volume 127)
54)] ÁFAB ¼ À lnheÀ½EA ÀEB iB ð64Þ In fact, Eq. (62) holds irrespective of the switching time ts : The equilibrium freeenergy difference is determined by the spectrum of a quantity, WAB , associated with a nonequilibrium process. The ‘‘exponential average’’ of the work done in taking the system between the designated macrostates (at any chosen rate) thus provides an alternative estimator of the difference between the associated free energies. The fact that Eq. (62) (in general) folds in nonequilibrium processes is made explicit through a third result that may be deduced from it.
In summarizing it, we revert to the particular context of primary interest in which the two macrostates belong to different phases. The core idea is simple: to use ES methods to seek out regions of the conﬁguration space of one phase which are such that a transition (switch, leap) to the other will be accepted with reasonable probability. The leap avoids mixed-phase conﬁgurations: The simulation explores both conﬁguration spaces but is always to be found in one or the other. The full machinery of ESPS is customizable in a number of respects, notably the choice of reference conﬁgurations, of order parameter and of transformation matrix.
We discuss them in turn. First, the NIRM method hinges on the identiﬁcation of a good path and reference macrostate. A ‘‘good’’ path is short; but the reference macrostate (the choice of which is limited) may lie far from the physical macrostate of interest, entailing a large number of independent simulations to make the necessary link. In a sense the ESM provides a case in point: The reference macrostate is strictly located at l ¼ 1; corrections for the use of a ﬁnite l need to be made .