  In classical physics there is a well-known theorem in which it is established
that the energy per degree of freedom is the same. However, in quantum
mechanics due to the non-commutativity of some pairs of observables and the
possibility of having non-Markovian dynamics, the energy is not equally
distributed. We propose a correspondence between what we know about the
classical energy equipartition theorem and its possible counterpart in
phase-space formulation in quantum mechanics based on the Wigner
representation. Also, we show that in the high-temperature regime, the
classical result is recovered.
