Entropy theory distribution computation

There is thus assumed to be a one-to-one correspondence between the most probable distribution and the thermodynamic state. The equilibrium ensemble corresponding to any given thermodynamic state is then used to compute averages over the ensemble of other (not necessarily thermodynamic) properties of the systems represented in the ensemble. The first step in developing this theory is thus a suitable definition of the probability of a distribution in a collection of systems. In classical statistics we are familiar with the fact that the logarithm of the probability of a distribution w[n is — J(n) w n) In w n, and that the classical expression for entropy in the ensemble is20... 

The derivation of the entropy in terms of the long-wavelength composition fluctuations seems to need no generalization to time-dependent temperature variations. However, the composition correlations which appear in the entropy expression will not respond fully and in phase with a rapid temperature variation, and a computation of this response is now necessary for a computation of the dynamic heat capacity. It will be supposed, as in the theory of the viscosity, that the radial distribution function satisfies the generalized diffusion equation... 

Though the etqxment v is close to the experimmital value, the prediction of this theory for other quantities turns out to be inadequate for example, the expression for Ae free energy (eqn (2.98)) is not consistent with the distribution function of the end-to-end vector obtained by computer simulation. Also it suffras from an unreasonable behaviour of the entropy. -----... 

Perhaps Clausius hoped to, but did not, provide a way of computing N associated with irreversible processes. Nineteenth-century thermodynamics remained in the restricted domain of idealized reversible transformation and without a theory that related entropy explicitly to irreversible processes. Some expressed the view that entropy is a physical quantity that is spatially distributed and transported (e.g. Bertrand [7] in his 1887 text), but still no theory relating irreversible processes to entropy was formulated in the nineteenth century. 

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