Generalised energy equipartition in electrical circuits

Abstract

In this brief note, we demonstrate a generalised energy equipartition theorem for a generic electrical circuit with Johnson-Nyquist (thermal) noise. From quantum mechanical considerations, the thermal modes have an energy distribution dictated by Planck's law. For a resistive circuit with some inductance, it is shown that the real part of the admittance is proportional to a probability distribution function which modulates the contributions to the system's mean energy from various frequencies of the Fourier spectrum. Further, we analyse the case with a capacitor connected in series with an inductor and a resistor. The results resemble superstatistics, i.e. a superposition of two statistics and can be reformulated in the energy representation. The correct classical limit is obtained as $\hslash \to 0$.

v2: Typos corrected

References in corpus (3)

• Quantum partition of energy for a free Brownian particle: Impact of dissipation
• Quantum counterpart of energy equipartition theorem for a dissipative charged magneto-oscillator: Effect of dissipation, memory, and magnetic field
• Partition of free energy for a Brownian quantum oscillator: Effect of dissipation and magnetic field

Cited by in corpus (4)

• Independent-oscillator model and the quantum Langevin equation for an oscillator: A review
• Quantum dissipation and the virial theorem
• Quantum Counterpart of Equipartition Theorem in Quadratic Systems
• Quantum Counterpart of Equipartition Theorem: A Möbius Inversion Approach