Use of Semigrand Partition Functions

When a system at specified T and P contains two species and one of them is in equilibrium with that species in a reservoir through a semipermeable membrane, the transformed Gibbs energy of the system is calculated from the semigrand partition function F(7( P, /q, N2) by use of... 

The semigrand partition function can be written for a system of biochemical reactions at specified concentrations of coenzymes, and G" = —kT n T". The fundamental equation for G" can be used to calculate the other thermodynamic... 

This semigrand partition function approach as phrased in the context of KB theory thus allows one to obtain average structural information from thermodynamic data. We have made some series truncation approximations and so we must ask to what extent the success of the method depends on our assumptions. To consider this we turn to simulation and calculate some of the quantities we have derived. Simulation is, of course, always model dependent but this gives an otherwise independent view of the success of our low-order activity series theory. In particular, by using the ratio of partition functions as parameters in an activity series expansion for quantities such as N2) we must address whether these are the real coefficients or effective coefficients, which have considerable contributions or take up the slack from higher-order terms in the series. So for instance, at infinite dilution we can write... 

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