Equipartition's energy theorem

[Talker1500]

Hi,

I'm reading about the equipartition's energy theorem (classical statistics), and I was wondering about its validity when applied to different hamiltonians.

The usual case, H=p ^2/2m, it yields 3/2KT in 3D, but what about more complicated H? Like H=|p|c, or a H with a complex V? would the theorem still be available for use?

Thanks

 

[Marioeden]

Equipartition of energy is only valid for a potential free system.

Beyond that you may want to look up the Virial Theorem

 

[nasu]

It seems to work for harmonic potentials, if the temperature is high enough.
See specific heats of solids (in harmonic approximation, high temperature limit).
Or this:
http://en.wikipedia.org/wiki/Equipartition_theorem

 

[jasonRF]

In 1-D is isn't too hard to derive the result for the cases H = |p|, or H = p^4. The derivation closely follows that of the quadratic case. In 3-D I suspect it is much more complicated, but I am often wrong!

jason

 

[Jorriss]

The 'usual' Equipartition says that each quadratic degree of freedom in the Hamiltonian contributes 1/2KT, but there is a more general Equipartition theorem that can be used (usefully) in more situations.

http://en.wikipedia.org/wiki/Equipartition_theorem#The_microcanonical_ensemble