Assumptions

We begin by outlining the assumptions which enable the canonical derivation of the master equation. Our general assumption is that our system is a harmonic oscillator ( $aa^{\dagger}$) which interacts with a bath of oscillators ( $\sum_i b_ib_i^{\dagger}$). Specifically:

1. We assume that the energy spectrum of the bath of oscillators is spaced tightly enough relative to its overall domain, i.e. $\omega_i \ll (\omega_{N} -\omega_{0})$ such that the approximation $\sum_i \rightarrow \int d\omega_i g(\omega_i)$, where $g(\omega_i)$ is the density of states of the reservoir, is a physically acceptable mathematical assumption.
2. Related to the previous assumption, we assume that the bath is large enough and in a state of equilibrium such that any perturbations caused by the individual system on the bath is negligible. This is to say, the future state of the system-bath density operator is determined by its current state, and is not a function of the history of the bath (that is, we assume $\rho_{sb}=\rho_s(t)\otimes \rho_b(0)$).This is the Markoffian assumption.
3. We assume the rotating wave approximation regime. The interaction of the bath and system will have terms such as $ab, a^{\dagger}b,ab^{\dagger}, a^{\dagger}b^{\dagger}$. The lowering-lowering and raising-raising coupling has a much slower varying contribution to the state of the system, and so are excluded to give the interaction Hamiltonian $\sum_i g_i \left(a^{\dagger}b_i + ab_i^{\dagger}\right)$ where $g_i$ is a real coupling constant. Obviously, one must be certain the system one models can be simplified as such in order to apply the general master equation.