Eur. Phys. J. B 31, 249-257 (2003)
https://doi.org/10.1140/epjb/e2003-00029-3

Distribution of local entropy in the Hilbert space of bi-partite quantum systems: origin of Jaynes' principle

Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

Corresponding author: ^a jochen@theol.physik.uni-stuttgart.de

Received: 13 June 2002
Revised: 14 November 2002
Published online: 4 February 2003

Abstract

For a closed bi-partite quantum system partitioned into system proper and environment we interpret the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible pure-state trajectories are confined to certain regions in Hilbert space. We show that in a properly defined thermodynamical limit almost all states within those accessible regions represent states of some maximum local entropy. For the microcanonical condition this dominant state still depends on the initial state; for the canonical condition it coincides with that defined by Jaynes' principle. It is these states which thermodynamical systems should generically evolve into.