A heuristic derivation, e.g., in the notes by Preskill, begins with a more general form of an open quantum system and converts it into Lindblad form by making the Markovian assumption and expanding in small time. A more physically motivated standard treatment covers three common types of derivations of the Lindbladian starting from a Hamiltonian acting on both the system and environment: the weak coupling limit (described in detail below), the low density approximation, and the singular coupling limit. Each of these relies on specific physical assumptions regarding, e.g., correlation functions of the environment. For example, in the weak coupling limit derivation, one typically assumes that (a) correlations of the system with the environment develop slowly, (b) excitations of the environment caused by system decay quickly, and (c) terms which are fast-oscillating when compared to the system timescale of interest can be neglected. These three approximations are called Born, Markov, and rotating wave, respectively.