I've wanted to do some writing about statistical mechanics, but it's difficult to do without it turning into deathly boring strings of equations. There's ways to make it interesting, I'm sure, and I think webcomic artist Randal Munroe has found one:

Full size at the link. "Hmm," thought I when I read it. "that sounds about right. Where's the factor of 2 from?" It's a reflection of the fact that it takes two to tango, as it were, and so you have to convert the population density into tango density.

But really for certain unorthodox folks that 2 may not be accurate. Maybe they enjoy those weird practices with French names. And those are less common, and so you'll have to express the stuff under the radical in terms of weight factors denoting how they vary with respect to people/act.

In a wildly different (but mathematically similar) physics context we call this the density of states. When tracking the physics of how energy is distributed among the members of a statistical ensemble, you have to consider the fact that there may be more than one state with the same energy. You must integrate over the density of states to actually derive the thermodynamics of those systems.

Practically speaking I don't think it would make much of a difference here. There can't possibly be all that many people engaging in S > 2 acts.

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Think of it as a small-angle approximation (rimshot.)

Why are you ignoring the S < 2 case?

At least, that many people outside the associated film industry....

DCS: Munroe (2009) assumes that the S = 1 case is trivial. But I suppose that depends on your definition of what constitutes an S = 1 case.

D.C.: I think this is where I make a pun about degeneracy, but I had better leave well enough alone...

That depends on whether the analysis is hyperbolic -- if you want the

reallydegenerate case, consider S=0...

But all things considered, it might be best to not blog on the subject.