Nyquist and Callen-Welton fluctuation-dissipation theorem as a consequence of detailed balance principle applied for a resonance RLC-circuit

The Callen-Welton and Nyquist theorems in the statistical physics are re-derided in a thermodynamic style using detailed balance principle applied for the thermal averaged energy of a high Q-factor RLC resonance circuit. The usual proof requires a standard statistical averaging of the perturbation theory expression for the generalized susceptibility, while the detailed balance principle gives much shorter derivation appropriate for all university courses of thermal or statistical physics. In the framework of the new approach, the Callen-Welton theorem is a consequence of the Nyquist theorem, while in the traditional approach the Nyquist theorem is an interesting application of the Callen-Welton.