  The transition from reversible microdynamics to irreversible transport can be
studied very efficiently with the help of the so-called projection method. We
give a concise introduction to that method, illustrate its power by using it to
analyze the well-known rate and quantum Boltzmann equations, and present, as a
new application, the derivation of a source term accounting for the spontaneous
creation of electron-positron pairs in strong fields. Thereby we emphasize the
fundamental importance of time scales: only if the various time scales
exhibited by the dynamics are widely disparate, can the evolution of the slower
degrees of freedom be described by a conventional Markovian transport equation;
otherwise, one must account for finite memory effects. We show how the
projection method can be employed to determine these time scales, and how --if
necessary-- it allows one to include memory effects in a straightforward
manner. Finally, there is an appendix in which we discuss the concepts of
entropy and macroscopic irreversibility.
