# Equipartition's energy theorem

1. Jun 26, 2013

### 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

2. Jun 26, 2013

### Marioeden

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

Beyond that you may wanna look up the Virial Theorem

3. Jun 26, 2013

### 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

4. Jun 27, 2013

### 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

5. Jun 27, 2013