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

• URL: http://arxiv.org/abs/2205.12364v2
• Date: Mon, 7 Nov 2022 19:55:11 GMT
• Title: Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics
• Authors: Esteban Marulanda, Alejandro Restrepo, Johans Restrepo
• Abstract summary: In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
• Score: 62.997667081978825
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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