where L T [•] is the Liouvillian superoperator that acts on operators and [•, •] is the commutator between two operators. When the quantum system of interest interacts with a large environment, the dynamics of the composite system and environment is generally too complicated and computationally expensive to keep track of in full detail. Instead, the dynamics of the system alone can be tracked using the reduced density matrix ρS (associated with ĤS in Eq. 1) defined as follows