Subdynamics of constrained many-body systems and the theory of transport coefficients

Abstract

The concept of subdynamics previously introduced for homogeneous systems by our group is extended to the case of constrained systems. The case of a plasma in an external electric field is studied in detail. For this purpose, we introduce projection operators II (o) E and II (∨) E depending on the external field. The interest of this generalization appears when we show that the steady current for weak stationary external fields depends only on the II (o) E component of the N-body distribution function. Another very important consequence of our calculations is that we give a rigorous mathematical derivation for the standard formula which gives the steady current in a weak stationary and homogeneous field. The Chapman-Enskog derivation is recovered and very naturally generalized in the II (o) E framework.