A systematic projection operator formalism in nonequilibrium statistical mechanics

A systematic damping theoretical formalism is presented to give basic equations of statistical physics. Our formalism naturally yields the so-called time convolution (TC) and time convolutionless (TCL) equations both for a density matrix and for dynamical variables. The method is explicitly used to obtain equations in the Heisenberg picture (equations of motion for dynamical variables). In contrast to the existing derivation of equations of motion, the present formalism gives a systematic method for deriving these equations without specifying the projection operator. Moreover, the formalism is valid even for time-dependent Hamiltonian systems. A simple example is given to illustrate our formalism.