Gibbs canonical partition function

The Gibbs canonical partition function of this chain is given by the expression... 

The thennodynamic properties of a classical hard-sphere system are derivable from the Gibbs canonical partition function... 

Note first that the canonical partition function (Eq. (75)) for the nonrelativistic ideal gas for the Boltzmann-Gibbs statistics can be rewritten as... 

We can express the Gibbs energy by relation [5.42]. The molecules of the solid are therefore considered as distinguishable molecules the canonical partition function is therefore given by relation [5.15]. So relation [6.125] becomes ... 

The canonical partition function Z in statistical thermodynamics is fundamental since it is related to thermodynamic parameters like enthalpy and Gibbs energy. For instance, the Gibbs free energy is given by ... 

Consider a system of N particles in volume V. Assume that the temperature T of the system is constant. The ensemble of microscopic points in phase space that correspond to this NVT macroscopic state is called the ATT or canonical ensemble. The canonical ensemble is called that simply because it was the first ensemble tackled by Gibbs. Indeed, ensemble theory as described in Gibbs seminal text (see Further reading) was formulated entirely for the constant temperature ensemble. The reason, as will become apparent in this chapter, is the ease in determining the canonical partition function. 

There are four main ensembles in statistical thermodynamics for which the independent variables are NVE (microcanonical), NVT (canonical), NpT (Gibbs or isothermal isobaric), and VT (grand canonical). The characteristic fnnetions provided in Equations 1.2 and 1.3 can be expressed in terms of a series of partition functions such that (Hill 1956)... 

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