Reduced Density Matrix and its Equation of Motion

Notice that the Hamiltonian of the total (or isolated) system can be expressed as [3-5,18] 

Let a represent the density matrix of the system which is usually referred to as the reduced density matrix and is obtained by eliminating the heat bath variables [3-5,18,19] 

To obtain pmvir/ introduce the projection operator D so that 

To obtain p, the Laplace transformation method (see Section 2) can be used, i.e., 

To simplify Eq. (3.32) which is exact, one needs additional conditions. Suppose that 

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