Conceivably there could be interactions which are sufficiently constrained to prevent the equipartition theorem from coming into play in practice. For example,

Conceivably there could be interactions which are sufficiently constrained to prevent the equipartition theorem from coming into play in practice. For example, an interaction with a massive carrier may not be able to support thermal transfer except at very high energies. Gravitational heat transfer would, I assume, work for everything, but it would also be very very slow. We're a little bit spoiled by EM - it makes thermal interactions happen quickly and at all energy scales.