On the interpretation and significance of the fluctuation–dissipation theorem in infrared spectroscopy

In this paper we revisit the classical fluctuation–dissipation theorem with derivations and interpretations based on quantum electrodynamics (QED). As a starting point we take the widely cited semiclassical expression of the theorem connecting the absorption coefficient with the correlation spectra of a radiating molecular dipole. The literature is suggesting how this connection can be derived in terms of quantum mechanical statistical averages, but the corresponding results in terms of QED seems to be very difficult to trace in detail. The problem is therefore addressed here based on first principles. Interestingly, it turns out that the QED approach applied to the aforementioned statistical averages does not only prove the validity of the fluctuation–dissipation theorem, but it also provides a derivation and a quantum mechanical interpretation of Schwarzschild’s equation for radiative transfer. In particular, it is found that the classical Beer–Bouguer–Lambert law is due to absorption as well as of stimulated emission, and furthermore that the source term in Schwarzschild’s equation (Kirchhoff’s law) is due solely to spontaneous emission. The significance of the fluctuation–dissipation theorem is finally elaborated on in terms of the appropriate scaling of line strength parameters (including line mixing) which is relevant in far infrared and millimeter wave broadband applications.