We have generalized Einstein coefficients and rate equations from quantum field theoretic point of view by bringing the fundamental processes and the quantum Rabi oscillation in a single footing for the light–matter interactions for nonzero Rabi frequency. We have analytically obtained multimode Jaynes–Cummings model results for the quantum Rabi oscillation of a two-level system in a lossy resonant cavity containing (i) thermal photons and (ii) injected photons of a coherent field. We have renormalized the coupling constant for the light–matter interactions for these cases. Our results match well with the seminal experimental data obtained in this regard by Brune et al (1996 Phys. Rev. Lett. 76 1800). We also have studied the population dynamics in this regard by applying the generalized Einstein rate equations.

Starting from the Rabi Hamiltonian, which is useful to get non-perturbative results within the rotating wave approximation, we have obtained the Einstein's B coefficient to be time-dependent, B(t) ∝ |J0(ωγ t)|, for a two-level system (atom or molecule) in the thermal radiation field. Here ωγ is the corresponding Rabi flopping (angular) frequency and J0 is the zeroth order Bessel function of the first kind. The resulting oscillations in the B coefficient -even in the limit of very small ωγ -drives the system away from the thermodynamic equilibrium at any finite temperature in contrary to Einstein's prediction. The time-dependent generalized B coefficient facilitates a path to go beyond the Pauli's formalism of non-equilibrium statistical mechanics involving the quantum statistical Boltzmann (master) equation. We have obtained the entropy production of the two-level system, in this context, by revising Einstein's rate equations considering the A coefficient to be the original time-independent one and B coefficient to be the time-dependent one.

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