Nonequilibrium statistical quantum field theory for open systems

Recently, a number of authors have begun to study the evolution of quantum fields in the early Universe characterized by a time-dependent density matrix rho/sub S/(t). All of this work is predicated on the assumption that one's ''subsystem'' of interest is in some sense ''decoupled'' from the rest of the Universe, so that rho/sub S/ satisfies a Liouville--von Neumann equation which implies, e.g., an isentropic evolution. Starting from ''first principles,'' i.e., the Schroedinger equation for the totality of ''subsystem'' plus surroundings (''bath''), it is shown here how such a picture can be derived as the limiting case of a more complete statistical description. Quite generally, one finds that rho/sub S/ and the ''bath'' density matrix rho/sub B/ satisfy coupled nonlinear generalizations of the Liouville--von Neumann equation and evidence a nonisentropic evolution. However, in a Vlasov-type approximation, rho/sub S/ and rho/sub B/ satisfy instead much simpler bilinear equations which imply an isentropic evolution. And finally, in the limit that the ''back reaction'' of rho/sub S/ on rho/sub B/ can be neglected in computing the evolution of rho/sub B/, one recovers a true Liouville--von Neumann equation for the evolution of rho/sub S/ in an external field