Statistical mechanics of a large dynamical system interacting with an external time-dependent field: generalised correlation subdynamics

We recently showed that it is possible, using an explicitly time-dependent formalism, to separate the density matrix (or distribution function) ϱ of a large, isolated dynamical system into a complete set of mutually orthogonal projections ?, each obeying its own independent subdynamics. In the presence of an external, time-dependent field these ? subspaces are themselves coupled. For this situation, we now obtain, under mild integrability conditions, the new time-dependent projectors ?, for the complete set of generalised correlations ν, under which the projections ?ρ( t) again obey independent subdynamics. This result is a generalisation of the work of Balescu and Misguich, which was confined to the vacuum case (ν=0). It considerably broadens the scope of the subdynamics theory, which may now be applied to the study of irreversible processes in macroscopic systems evolving under the influence of external fields. Such ramifications will be discussed in future publications.