# Feynman Lectures and the Zeroth Law of Thermodynamics

In Volume 1 of the Feynman Lectures on Physics, Feynman derives the ideal gas law from Newton's laws of motion. But then on page 41-1, he puts a caveat to the derivation he has just completed: "We have perpetually been making a certain important assumption, which is that if a given system is in thermal equilibrium at a given temperature, it will also be in equilibrium with anything else at the same temperature ... This proposition is true and can be proven from the laws of mechanics, but the proof is very complicated and can be established only by using advanced mechanics. It is much easier to prove in quantum mechanics than it is in classical mechanics. It was proved first by Boltzmann, but for now we simply take it to be true."

Does anyone know what Feynman is talking about? Is he referring to the Zeroth Law of Thermodynamics? Can it be proved using Newton's laws of motion, and is the proof really complicated? Where can I find this proof?

Any help would be greatly appreciated.
Thank You in Advance.

## Answers and Replies

I've done some reading about Boltzmann, and I'm thinking that this may have something to do with the equipartition theorem. Is the equipartition theorem in any way connected to the zeroth law?

I think you have it right - its the zeroth law of thermodynamics.

The proof of the zeroth law is complicated - because it involves showing that there is a function of the (macroscopic) thermodynamic variables which can be used to define equilibrium (this function is the temperature) starting from microscopic variables (for instance the positions and momenta of all the molecules making up a gas).

I think you have it right - its the zeroth law of thermodynamics.

The proof of the zeroth law is complicated - because it involves showing that there is a function of the (macroscopic) thermodynamic variables which can be used to define equilibrium (this function is the temperature) starting from microscopic variables (for instance the positions and momenta of all the molecules making up a gas).
Where can I find this proof of the zeroth law from Newton's laws? Why does it require "advanced mechanics" (which I assume refers to Lagrangians and Hamiltonians) and why is it easier if you start from quantum mechanics instead?