Generalised energy equipartition in electrical circuits

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