Re-examining Einstein's B coefficient and rate equations with the Rabi model

Starting from the Rabi Hamiltonian, which is useful in arriving at non-perturbative results within the rotating wave approximation, we have found Einstein's B coefficient to be time-dependent: B(t)propto|J₀\(ω_γt\)| for a two-level system (atom or molecule) in thermal radiation field. Here ω_γ 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 for very small ω_γ---drives the system away from thermodynamic equilibrium at any finite temperature contrary to Einstein's assumption. The time-dependent generalized B coefficient facilitates a path to go beyond Pauli's formalism of non-equilibrium statistical mechanics involving the quantum statistical Boltzmann (master) equation. In this context, we have obtained entropy production of the two-level system by revising Einstein's rate equations, while considering the A coefficient to be the original time-independent one and the B coefficient to be time-dependent.