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

Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics