Entropy bottleneck

R. A. Marcus My interests in variational microcanonical transition state theory with J conservation goes back to a J. Chem. Phys. 1965 paper [1], and perhaps I could make a few comments. First, using a variational treatment we showed with Steve Klippenstein a few years ago that the transition-state switching mentioned by Prof. Lorquet poses no major problem The calculations sometimes reveal two, instead of one, bottlenecks (transition states, position of minimum entropy along the reaction coordinate) [2], and then one can use a method described by Miller and partly anticipated by Wigner and Hirschfelder to calculate the net dux. 

Liquids and proteins are complex systems for which the smdy of dynamical systems has wide applicability. In the conference, relaxation in liquids (s-entropy by Douglas at the National Institute of Standards and Technology, nonlinear optics by Saito, and energy bottlenecks by Shudo and Saito), energy redistribution in proteins (Leitner and Straub et al.), structural changes in proteins (Kidera at Yokohama City University), and a new formulation of the Nose-Hoover chain (Ezra at Cornell University) were discussed. Kidera s talk discussed time series analyses in molecular dynamics, and it is closely related to the problem of data mining. In the second part of the volume, we collect the contributions by Leitner and by Straub s group, and the one by Shudo and Saito in the third part. 

Internally equilibrated subsystems, which act as free energy reservoirs, are already as random as possible given their boundary conditions, even if they are not in equilibrium with one another because of some bottleneck. Tlius, the only kinds of perturbation that can arise and be stabilized when they are coupled are those that make the joint system less constrained than the subsystems originally were. (This is Boltzmann s H-theorem [9] only a less constrained joint system has a liigher maximal entropy than die sum of entropies from the subsystems independently and can stably adopt a different form.) The flows that relax reservoir constraints are thermochemical relaxation processes toward the equilibrium state for tlte joint ensemble. The processes by wliich such equilibration takes place are by assumption not reachable within the equilibrium distribution of either subsystem. As the nature of the relaxation phenomenon often depends on aspects of the crosssystem coupling that are much more specific than the constraints that define either reservoir, they are often correspondingly more complex than the typical processes... 

Variational transition state theory (VTST) is useful when no TS can be explicitly identified (for Morse-like potential, e.g., direct bond dissociation), where there is no TS. It is based on the idea that there is a bottleneck in the phase space during the dissociatioa This can be explained by the fact that during the dissociation process the molecule needs to reach at a certain point a very specific conformation, without which it cannot go further to disassociate. The Arrhenius equation can be written in terms of exponential of Gibbs free energy and exponential of entropy, which characterize the nmnber of distinct states reachable with that amount of energy. 

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