Degrees of Freedom

• Phase space is 6-Dimensional. This is the maximum # of degrees of freedom.

• Adiabatic invariants involve an average over one of these dimensions.

• Time is NOT a degree of freedom. For one thing, diffusion in all 6 phase space dimensions is possible. Time does not diffuse. In PDE’s it introduces a parabolic dimension, d/dt = d2/dq2. One can always add a homogeneous solution, 0 = d2/dq2