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 ?? 0 . � 2023, Indian Academy of Sciences.