production and the backreaction equations in a self-consistent manner (Hartle and Hu 1979). However the conditions for calculating the in-out vacuum persistence amplitude are unsuitable for the consideration of backreactions, as the effective equations are acausal and complex. The second major step was the recognition by DeWitt (1986), Jordan (1986), and Calzetta and Hu (1987) that the in-in or closed-time-path formalism of Schwinger (1961) and Keldysh (1964) is the right way to go. Calzetta and Hu (1987) derived the backreaction equations for conformal scalar fields in Bianchi I universe, which provided a beachhead for later discussion of the semiclassical limit of quantum cosmology. They also recognized the capacity of this framework in treating both the quantum and statistical aspects of dynamical fields and indeed used it for a reformulation of non-equilibrium statistical field theory (Calzetta and Hu 1988). The third step in making the connection with statistical mechanics is the construction of the so-called coarse-grained effective action by Hu and Zhang (1990), similar in spirit to the well-known projection operator method in statistical mechanics (Zwanzig 1961).

This is where the connection with ‘quantum open systems’ first enters. The general idea behind the study of such systems is that one starts 