Entropy-variation with resistance in a quantized RLC circuit derived by the generalized Hellmann－Feynman theorem

By virtue of the generalized Hellmann--Feynman theorem for the ensemble average, we obtain the internal energy and average energy consumed by the resistance R in a quantized resistance--inductance--capacitance (RLC) electric circuit. We also calculate the entropy-variation with R. The relation between entropy and R is also derived. By the use of figures we indeed see that the entropy increases with the increment of R.