Gibbsian ensembles

Statistical thermodynamics gives us the recipes to perform this average. The most appropriate Gibbsian ensemble for our problem is the canonical one (namely the isochoric-isothermal ensemble N,V,T). We remark, in passing, that other ensembles such as the grand canonical one have to be selected for other solvation problems). To determine the partition function necessary to compute the thermodynamic properties of the system, and in particular the solvation energy of M which we are now interested in, of a computer simulation is necessary [1],... 

Our perspective is that the PDT should be recognized as directly analogous to the partition functions which express the Gibbsian ensemble formulation of statistical mechanics. From this perspective, the PDT is a formula for a thermodynamic potential in terms of a partition function. Merely the identification of a... 

Information-theoretic distributions constracted in the above-described marmer are identical in form to the distributions for the various quantum and classical Gibbsian ensembles discussed earlier. This can be traced to the formal eqtrivalence of the missing information / and the Gibbs entropy S. As with information-theoretic distributions, the Gibbsian distributions are maximum entropy distributions consistent with the information defining the macroscopic state of a system. 

From the above discussion, it should be clear that all of the classical probability densities for the various Gibbsian ensembles discussed earlier can be constracted by starting with the maximum entropy principle and making use of the information defining the macroscopic state of the system. 

The correction displayed is negligible relative to 1, in the macroscopic limit. The independence in the thermodynamic limit of the PDT on a choice of simulation ensemble used for statistical evaluation is a difference from the partition functions encountered in Gibbsian statistical thermodynamics. 

Usually DSC experiments are performed on ideally diluted aqueous solutions of proteins in which each macromolecule can be assumed to experience minimal interactions with the others. This means that such a solution can be viewed to a good approximation as an ensemble of non-interacting small microscopic systems in the Gibbsian sense. 

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