Quantum Counterpart of Equipartition Theorem in Quadratic 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.

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References in corpus (9)

• Heat Transistor: Demonstration of Gate-Controlled Electron Refrigeration
• Barrow's black hole entropy and the equipartition theorem
• Quantum partition of energy for a free Brownian particle: Impact of dissipation
• On the Limiting Cases of Nonextensive Thermostatistics
• Quantum counterpart of energy equipartition theorem for a dissipative charged magneto-oscillator: Effect of dissipation, memory, and magnetic field
• Partition of kinetic energy and magnetic moment in dissipative diamagnetism
• Generalised energy equipartition in electrical circuits
• Multimode Brownian oscillators: Exact solutions to heat transport
• On the Generalised Equipartition Law

Cited by in corpus (2)

• Explicit noise and dissipation operators for quantum stochastic thermodynamics
• Quantum Counterpart of Equipartition Theorem: A Möbius Inversion Approach