The typical reduced state of the system

Abstract

In Chap. 8 we found that there is no typicality of the full state of the non-composite system. In this chapter we investigate whether or not there is typicality of the reduced state of some considered system which interacts with some sort of environment. This question is answered for couplings that may exchange energy between system and environment and couplings that cannot. It is essentially found that, roughly speaking, large environments yield typical reduced states of the system. Those typical states turn out to be, e.g., the Boltzmann equilibrium state under microcanonical or the Gibbs equilibrium state under canonical conditions. Thus the composite system scenario may give rise to standard thermodynamical relaxation of the whole considered system, including increase of local entropy. © 2009 Springer-Verlag Berlin Heidelberg.