I was wondering what are the sufficient conditions for the Equipartition Theorem. I know there is another question (For which systems is the equipartition theorem valid?) that somewhats answers this question, but it only addresses the need for the system to be in thermal equilibrium.
However, I was wondering if the system has to be ergodic as well. I've read this in several places before however I haven't been able to find a good explanation or derivation of the Equipartition Theorem that mentions the system must be ergodic. I was wondering if this actually is true and if so, could anyone direct me to an explanation of why or provide an original one. Thanks.