> Incidentally, one formulation I've run across online is that the
> "Hamiltonian" refers to the (6N-1)D surface in (6N)D phase space with
> constant energy, with the (as it turns out) first law of thermodynamics
> referring to a constraint on the trajectory through phase space; i.e., any
> individual point must move along the Hamiltonian hypersurface that has
> constant energy.
Don't forget, position in phase space fully determines the future
trajectory (in the classical model). Phase space points represent
positions plus velocities. Given a point, you can trace the line
which the system will follow. In this model there is little need for
a hypersurface of constant energy. You could define one, but it's not
really very meaningful since you already know exactly where on that
surface it is going to go, given the initial position in phase space.
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