Partition nonequilibrium

The probability distribution is normalized by ZM( p, t), which is a time-dependent partition function whose logarithm gives the nonequilibrium total entropy, which may be used as a generating function. 

The Kolmogorov-Sinai entropy per unit time is defined in Eq. (89) as the supremum of h over all the possible partitions V. Since we expect that the probability of the nonequilibrium steady state is not time-reversal symmetric, the probability of the time-reversed paths should decay at a different rate, which can be called a time-reversed entropy per unit time [3]... 

Using a nonequilibrium approach, strong binding can be studied (ligand-receptor complex) (43). However, of particular interest in ACE and MACE is the characterization of weak interactions, since the rate of complex formation and the exchange of solute between aqueous and micellar phase could be too fast to be studied with conventional structure determination methods (MS, NMR). The alternative to those methods, namely, to measure in an equilibrium state, makes MACE highly attractive. Thus, weak bond strengths (acid-base and complex/partition equilibria) are measurable. 

In this system the bands (zones) broaden because of diffusion effects and nonequilibrium. This broadening mechanism is fairly symmetrical and the resulting elution bands approach the shape of a Gaussian curve. This system best explains liquid or gas partition chromatography. The system may be viewed in two ways ... 

In most cases we can assume that the equilibrium distribution and partitioning of organic chemicals in both mammalian and nonmammalian systems is a function of lipid content in the animal and that the lipid-water partition coefficient (AW) is equal to K0w Instances where this is not the case include specific binding sites (e.g., kepone in the liver) and nonequilibrium conditions caused by slow elimination rates of higher level organisms or structured lipid phases that sterically hinder accumulation of very hydrophobic chemicals. For aquatic organisms in constant contact with water, the bioconcentration factor or fish-water partition coefficient (AW) s simply ... 

The nonequilibrium equivalent of Equation (1.161) can be obtained using two alternative but equivalent schemes (often associated to the names of Pekar and Marcus). The two schemes are characterized by a different partition of the low and fast contributions of the apparent charges, namely we have [34] ... 

As two different partitions of the solvent charges are introduced, in order to obtain equivalent results, we have to use two different expressions for the nonequilibrium free energy, namely ... 

This partition and the subsequent nonequilibrium approach were originally formulated and commonly applied to electronic processes (for example solute electronic transitions) as well as to the evaluation of solute response to external oscillating fields [41], Such phenomena are discussed elsewhere in this book suffice it to say that in these cases the fast term is connected to the polarization of the electron clouds and the slow contribution accounts for all the nuclear degrees of freedom of the solvent molecules. 

As an example of a nonequilibrium partitioning process, let us work out the flux of a compound between the air over a lake and the water in the lake. This is an area of research that has been well studied, particularly for the transfer of PCBs into and out of the Great Lakes. Let us assume that the concentration of an organic compound in the air over the lake is Cair and the concentration in the water of the lake is Cwater- The flux between the water and the air is... 

In situ trace-element measurements of minerals from some of these peridotites provide a different perspective. The frequent presence of both fine-scale (100 p,m) zonation and nonequilibrium partitioning behavior for REE between many garnets and clinopyroxenes from Siberian peridotites (Shimizu etal, 1997 Shimizu, 1999)has two possible implications. One is the probable recent... 

Recent years have seen the extensive application of computer simulation techniques to the study of condensed phases of matter. The two techniques of major importance are the Monte Carlo method and the method of molecular dynamics. Monte Carlo methods are ways of evaluating the partition function of a many-particle system through sampling the multidimensional integral that defines it, and can be used only for the study of equilibrium quantities such as thermodynamic properties and average local structure. Molecular dynamics methods solve Newton s classical equations of motion for a system of particles placed in a box with periodic boundary conditions, and can be used to study both equilibrium and nonequilibrium properties such as time correlation functions. 

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