Dear xxxx,
In principle, one should say that there is no general mathematical rule relating fineness and tph, for cement just as for raw meal.
The reason is simply because this relation would be determined at least by two elements: the characteristics of the mill and the characteristics of the separator, if a closed circuit is assumed.
That's the reason also why, in principle, a mathematical should should used, like the Austin model.
Even in open circuit, there is no such general rule, because it depend on the mill and its charge and all its internals, and even the grinding aids. A very simple model would assume a specific power consumption proportional to the finenes, for low finenesses, and a saturation when the fineness reaches a certain level.
Strange enough, I think that a closed circuit might well be even simpler than an open circuit. In this case the mill tph tends to be more or less constant, more or less independently of the fineness of the finish product. (at least up a certain limit) Practically, it is not such a bad hypothesis to assuming power consumption proportional to the fineness, together with a constant mill power. But this need to be checked in each case.
For burnability and fineness, FLS and many others has published many paper on this topic. You will find many good thing by googling "burnability fineness". Have a look also at "Innovations in Portland Cement Manufacturing" from the PCA, where I guess you may find good material on these topics.