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arXiv · 2212.07024

Generalised energy equipartition in electrical circuits

Aritra Ghosh
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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 $\hbar \rightarrow 0$.

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BibTeXRIS

Aritra Ghosh. 2022-12-14. Generalised energy equipartition in electrical circuits. https://doi.org/10.1007/s12043-023-02553-w

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