Nonlinear Phenomena in Complex Systems, 2007, Vol.10, No.2, pp.192-195

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2007, Vol.10, No.2, pp.192-195

On the Basis of Quantum Statistical Mechanics.
A. Sugita

We propose a new approach to justify the use of the microcanonical ensemble for isolated macroscopic quantum systems. Since there are huge number of independent observables in a macroscopic system, we cannot see all of them. Actually what we observe can be written in a rather simple combination of local observables. Considering this limitation, we show that almost all states in a energy shell are practically indistinguishable from one another, and hence from the microcanonical ensemble. In particular, the expectation value of a macroscopic observable is very close to its microcanonical ensemble average for almost all states.
Key words: statistical mechanics, macroscopic quantum system

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