Entropy from cell theory

Note that the combination of solid-like and gas-like components is an alternative way to obtain the reduction in the entropy value from that in the gas state. In the cell theory of liquids, one uses an excluded volume to capture the constraint of the molecules. Here the reduction is obtained by giving a lower-than-unity value to the gas component. 

T AS are obtained from (AF — AH). In the right-hand half of the diagram the magnitude of — T AS is greater than that of AF, in accordance with electrostatic theory compare (24). As pointed out in Sec. 98, although the molecular dipoles in methanol are less numerous than in water, they lose more entropy in fact they lose so much more entropy that the term —T AS is predominant in producing the e.m.f. of the cells (198) placed back to back. 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

The first reason that led Latora and Baranger to evaluate the time evolution of the Gibbs entropy by means of a bunch of trajectories moving in a phase space divided into many small cells is the following In the Hamiltonian case the density equation must obey the Liouville theorem, namely it is a unitary transformation, which maintains the Gibbs entropy constant. However, this difficulty can be bypassed without abandoning the density picture. In line with the advocates of decoherence theory, we modify the density equation in such a way as to mimic the influence of external, extremely weak fluctuations [141]. It has to be pointed out that from this point of view, there is no essential difference with the case where these fluctuations correspond to a modified form of quantum mechanics [115]. 

The essence of the free-volume theory described in Section III is that the only change in free energy associated with a redistribution of free volume is in the entropy of the probability distribution of the free volume. This arises from the decomposition of the free energy into a sum of terms depending only on the volume of a single cell, the local free energy /(u,), and from the linearity of /(u,) in v, for liquidlike cells. Of the two, the former is the more serious approximation. 

Helfand [202, 208] suggested that Roe s work contained a number of assumptions, which made it difficult to appraise the applicability of the theory. Helfand suggested that Roe s lattice theory did not treat the conformational entropy properly by assuming that the chances of going from a cell site to any empty neighboring cell... 

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