Wide microstates

In this section we describe direct methods— those that enable one to calculate the absolute entropy of localized or wide microstates from a single sample. 

In several of the studies above, estimation of S was found to be unreliable, indicating that one must rely on the approximate alone. This is not a serious limitation, because, in general, one is interested in the difference in the free energy between two or more wide microstates, rather than in their absolute values. In many cases it has been found that such differences AF. b, 1) between the wide microstates i and j... 

Finally, it should be pointed out that because the transition probabilities are calculated in the LS method from the existing conformations and not from the future ones, the method is suited to handle a wide microstate that is defined on a limited region of conformational space (e.g., an a-helical... 

It would be of interest to extend the LS method and the hypothetical scanning method to MC and MD samples of continuum models of fluids (e.g., argon and water) and peptides in aqueous solutions. These methods enable one to calculate differences in free energy between significantly different wide microstates directly—that is, from two samples—and in principle, can handle even small differences in free energy of such microstates because the free energy fluctuations decrease with enhancement of the quality of the approximation. 

To put the previous statement into perspective it is necessary to stipulate that any macrosystem with well-defined values of its extensive parameters is made up of myriads of individual particles, each of which may be endowed with an unspecified internal energy, within a wide range consistent with all external constraints. The instantaneous distribution of energy among the constituent particles, adding up to the observed macroscopic energy, defines a microstate. It is clear that any given macrostate could arise as the result of untold different microstates. 

One would expect that lowering the temperature or increasing the viscosity of the solvent would increase the width of the lifetime distribution, since both factors may affect the rate of transitions between microstates. If this rate is high as compared with the mean value of the fluorescence lifetime, the distribution should be very narrow, as for tryptophan in solution. When the rate of transitions between microstates is low, a wide distribution would be expected. 

As argued by Fisher, pinned and sliding solutions can only coexist in some range of the externally applied force if the inertial term exceeds a certain threshold value [29]. This can lead to stick-slip motion as described in Section VI.A. For sufficiently small inertial terms, Middleton [85] has shown for a wide class of models, which includes the PT model as a special case, that the transition between pinned and sliding states is nonhysteretic and that there is a unique average value of F which does depend on vq but not on the initial microstate. The instantaneous value of Fk can nevertheless fluctuate, and the maximum of Fk can be used as a lower bound for the static friction force Fg. The measured values of Fj can also fluctuate, because unlike Fk they may depend on the initial microstate of the system [85]. 

Entropy is a measure of the total number of microstates in a system. There have been two widely used definitions of entropy, which were suggested by Ludwig Boltzmann and J. Willard Gibbs. We ll just look at the one specified by Boltzmann, since it s a little more straightforward to understand. The equation for Boltzmann s definition of entropy is ... 

Benitez RP, Silva MT, Klem J, Veznedaroglu E, Rosenwasser RH (2004) Endovascular occlusion of wide-necked aneurysms with a new intracranial microstent (Neuroform) and detachable coils. Neurosurgery 54 1359-1367... 

At any rate, even within these widely employed NMR protocols, computational approaches can play an important role. In particular, the choice among alternative structural hypotheses can often be guided by the correspondence between measured and computed spectroscopic parameters. Instances where this approach has led to disprove a seemingly reliable structural assignment are not uncommon. As a matter of fact, it is reasonable to foresee that this kind of validation will become even more widespread in the near future rather than any difficulty in the actual calculation of magnetic resonance parameters, stumbling blocks along this direction may be represented by issues of flexibility, protonation microstates, and... 

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