It might be better to say that the entropy is proportional to the logarithm...
This was Boltzmann's formulation. Of course Boltzmann used the term "thermodynamic probability" as equivalent to "number of ways." It is neither a thermodynamic quantity nor a probability; just a (big) number.
It is neither a thermodynamic quantity nor a probability; just a (big) number.Well, I guess that goes to show, a black hole is but a storm, full of sound and fury, signifying nothing. Then again, Shakespeare and thermodynamics probably don't mix...
Seriously though, when you say it's just a number, I assume you're referring to the fact that it's a coefficient? (just to make sure we're on the same page)