Generalized free energy

Following the notation of Eq. (9), a general free energy for chiral symmetry -breaking in membranes can be written as... 

In order to quantitatively compare the simulation with the continuum equation, we introduce a generalized free energy of the surface, and write the equation of motion in variational form. 

GENERAL FREE ENERGY CHANGES DE DONDER S AFFINITY 285... 

For arbitrary parameters of the system, wi and ho differ dramatically from each other one of them is 1, and the other is close to zero. Within a narrow range of parameters, however, they have the same order of magnitude and one can refer to a kinetic phase transition between the two stable states it is analogous to the first-order phase transition in an equilibrium system with a potential (in the absence of quantum fluctuations) playing the role of the generalized free energy of the system [42,65,110]. This is the range of parameters that is of particular interest in the present chapter. 

A generalized free energy of 998 42 cal. is calculated for the observed reactions involving a mole of any CeCd4i5000 structure with 1.5000 moles of liquid cadmium to give CeCd6i000. Specific free energies may be calculated from the... 

Second H-theorem When the distribution functional /[n,l] evolves in time according to the F-P equation (12) the generalized free-energy functional Falf] defined by... 

The general free energy expression (Eq. (3.16)) can be extended to the description of redox reactions by establishing the relations between EjJ and AG°. This can be done by the simple equation... 

There are many techniques of varying degrees of generality for the study of mechanisms and that of free energy relationships is the most readily applicable and general. Free energy relationships comprise the simplest and easiest of techniques to use but the results are probably the trickiest to interpret of all the mechanistic tools. 

The microscopic environment of the variant components (boxed in Scheme 2) would be approximately the same for both transition structure (TS) and protonated state (PS). As a corollary the microscopic medium effect in a general free energy relationship should be reduced if the model reaction chosen as standard closely resembles the reaction in question. In some cases it is useful to compare similar reactions, and an example of such a correlation is given in Problem 3. 

ATP serves as the general "free energy currency" for virtually all cellular processes. Hydrolysis of ATP is used to drive countless biochemical reactions, including many that are not phosphorylations. It is a direct source of energy for cell motility, muscle contraction, and the... 

The above calculation used free energies and the equilibrium constants for specific chemical reactions. For this reason the calculations apply only to the system, species, and reactions considered. It is possible to generalize free energy based equilibrium calculations so that they can be used with systems and species chosen arbitrarily, in a manner analogous to the program EQBRM described above. 

By assuming local equilibrium of the dissociation reactions, a zero free energy condition results which relates the local chemical potential of the neutral species to the charged species actually present. Thus, local equilibrium of reaction(21) implies the following generalized free energy equality... 

Their relative importance can be judged from the effect of temperature on the electromotive force. In the general free-energy equation (p. 67)... 

Garrett and Truhlar (1979) have shown that the minimum of kr T,s) corresponds to the maximum of the generalized free energy of activation curve,... 

CVT generalized free energy of activation gaussian-type orbital Hamiltonian Hessian... 

No more general free energy can be defined without the introduction of activity coefficients. 

This equation, a generalized free energy relationship for electron transfer (FERET), has the advantage of consisting entirely of terms that can be evaluated from experiment. This approach has been utilized for a comparative study of the inner sphere reactions of nitronium ions at an electrode and with aromatic substrates in solution, providing insight into the activation process. ... 

This density function provides the distribution of the particles centered around their lattice sites (Tarazona 1985). In this approach, the free energy is considered to be the functional F[p(r)] of the density distribution p(r) thus a general free energy functional can be expressed with the local density approximation as follows ... 

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