Quantum Counterpart of Equipartition Theorem in Quadratic Systems

TL;DR

This paper derives a quantum version of the generalized equipartition theorem for quadratic systems with multimode Brownian oscillators interacting with multiple reservoirs, extending classical principles into quantum regimes.

Contribution

It presents a novel derivation of the quantum equipartition theorem for complex quadratic systems, improving upon previous methods and confirming its reasonableness over alternative approaches.

Findings

Quantum equipartition theorem is applicable to multimode systems.

The quantum version provides a more reasonable energy description than alternative methods.

Results extend classical equipartition principles into quantum systems.

Abstract

The equipartition theorem is a fundamental law of classical statistical physics, which states that every degree of freedom contributes $k_{B}T/2$ to the energy, where $T$ is the temperature and $k_{B}$ is the Boltzmann constant. Recent studies have revealed the existence of a quantum version of the equipartition theorem. In the present work,we focus on how to obtain the quantum counterpart of the generalized equipartition theorem for arbitrary quadratic systems in which the multimode Brownian ocillators interact with multiple reservoirs at the same temperature. An alternative method of deriving the energy of the system is also discussed and compared with the result of the the quantum version of the equipartition theorem, after which we conclude that the latter is more reasonable. Our results can be viewed as an indispensable generalization of rencent works on a quantum version of the equipartition theorem.