Entropy criterion

This means that, to obtain the least variance in a multistage calculation, the intermediates should be constructed to have equal entropy difference for all stages. This criterion differs from the often used but unjustified rule of thumb that free energy differences should be equal in all stages [22,42], Simulation tests show that the entropy criterion leads to a great improvement in calculation precision compared to its free energy counterpart [26]. The same optimization criterion holds for calculation of entropy and enthalpy differences [44],... 

We show in Section II,C the relation between the L criterion and the entropy criterion and how the two criteria can be used to complement each other. 

An isolated system is one that exchanges neither matter nor energy with the surroundings. What is the entropy criterion for spontaneous change in an isolated system Give an example of a spontaneous process in an isolated system. 

It is more usual that a mechanistic interpretation can be given to AS for the reaction of a given compound only if there exists a body of thermodynamic data for a series of reactants for which mechanisms are known independently. An example of the latter sort is the entropy criterion for distinguishing between the A-l and the A-2 mechanism. 

As emphasized by Schaleger and Long [50], the entropy criterion must be exercised with caution . Considerable contributions to the overall AS value are due to solvation changes which take place in the formation of the transition state from the reactants. 

Zheng, X. M. Lu, W. M. Sun, D. Z., Enthalpy and entropy criterion for the molecular recognize of some organic compounds with beta cyclodextrin, Acta. Phys-Chim. Sin. 2001, 17, 343-347... 

From the full WPT we can generate a large number of possible redundant subtrees, or arbitrary WP trees (called wavelet bases). In fact, the total number of two-way (dyadic) bases is at least (2-)" for a tree depth equal to niev. For example, a dyadic WPT with tree depth niev = 12 has a library of at least 4.2 xlO bases The WPT has an important advantage compared with the WT because fast algorithms exist for the efficient search of the best wavelet basis, based on the minimisation of a cost function such as an entropy criterion. 

If the best-basis selection algorithm with the entropy criterion is applied to individual signals decomposed by WPT, the following situations can occur ... 

Once the variance tree is constructed, it can be searched for the joint best-basis, using the Coifman-Wickerhauser best-basis selection algorithm with, e.g., the entropy criterion. The entropy cost function (see Chapter 6) for the variance tree coefficients, which occur at the jth level in the i band of the signal decomposition is defined as ... 

For the Wilk s Lambda criterion, optimization was based on band(3,3), while the entropy criterion optimized over band(3,2). The CVQPM criterion optimized over the scaling band(3,0). Some features which we might expect from the adaptive wavelet algorithm, is that at termination, the band on which optimization was based would outperform the other bands, at least in... 

Optimization over the scaling band did improve the results slightly for the Wilk s Lambda and symmetric entropy criterion, but these criterion functions were not able to improve upon the results previously obtained with the CVQPM criterion function. 

We shall use the Schrbdinger representation which among other advantages reveals the temporal evolution of the density and provides a direct connection with standard quantum mechanics. Let us begin by considering only one observable A of interest. The maximum entropy criterion (Ref. [61] and IX-21 of Ref. [21]) provides the initial nonequilibrium density (f = 0)... 

However, the entropy criterion despite its significant interest carmot be the only criterion used. We must consider health impacts which may prohibit the physical recycling of certain waste because of infection risks or radioactivity. We may want to avoid excessive transportation and therefore process waste on site in an existing factoiy. Some processes of valorization require a large quantity of waste and a consistent quality that caimot always be maintained Economic aspects play an important role and may limit the use of a good solution if appropriate incentives are not implemented. 

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