# Equilibrium Stat Mech Vs. Kinetics

1. Jul 13, 2014

### bolbteppa

Ensembles

Figured it out thanks, next post:

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2. Jul 13, 2014

### bolbteppa

Related to this point (functioning as something which might explain the above more deeply), what is the actual meaning of this passage from Landau vol. 5:

Again as an example, take $H(q,p) = \tfrac{p^2}{2m}+\tfrac{k}{2}q^2 = E_0$ as the Hamiltonian for a single particle, the trajectory of the particle, i.e. the set of all possible states, is an ellipse in (q,p) phase space.

Extend it to n particles and we'll have a Cartesian product of n ellipses, or a big ellipsoid, visualized as

What in the world does that passage really mean, in terms of n harmonic oscillators respresented as a single curve in phase space? I can't make actually make any sense out of it.

3. Jul 13, 2014

### TSC

This is the ergodic hypothesis.