How did Ludwig Boltzmann develop the Boltzmann distribution and define entropy?

[Amok]

So this guy came up with the Boltzmann distribution and the statistical definition of entropy, where particles occupy discrete energy levels (or states) before the advent of quantum mechanics. How the hell did he do that, does anyone have any knowledge on how Boltzmann came up with the stuff he came up with? Or maybe he did not think of the states as being discrete?

 

[Dickfore]

Probability theory was a well developed mathematical field by the first half of the XIX century. The Boltzmann distribution is characteristic for classical particles for which the issue of indistinguishably is not essential. Boltzmann developed a kinetic equation which treated the collision between the particles for the first time. He also showed that a quantity he called H, and is related to the entropy of the gas, cannot increase if this equation holds. And, as you wondered correctly, the states are not discrete, so this quantity is determined up to an additive constant, just like entropy in Thermodynamics. He committed suicide, btw.

 

[Amok]

Ok... I was just wondering about that because most derivations and statements of the Boltzmann distribution found on the net and in books (at least the ones I've come across) use discrete energy levels. Take a look at wikipedia's page on the distribution, for example.