(i) For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given realistic observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and nonequilibrium conditions. In other words, there is a huge set of pure states (zero entropy) each of which imitates a given statistical ensemble to the extent that experimentally it is practically impossible to see a difference.
(ii) We demonstrate the equilibration of isolated macroscopic
quantum systems, prepared in non-equilibrium
mixed states with significant population
of many energy levels,
and observed by instruments with
a reasonably bound working range compared
to the resolution limit.
Both properties are fulfilled under many,
if not all, experimentally realistic
At equilibrium, the predictions and limitations of
Statistical Mechanics are recovered.
In other words, equilibrium Statistical Mechanics is derived from
standard Quantum Mechanics without any additional ``principle''
or ``postulate'' apart from the above mentioned assumptions about
realistic observables and initial conditions (work in progress).
A Uniqueness-Theorem for "Linear" Thermal Baths
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Phys. Rep. 361, 57 (2002)
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New J. Phys. 12, 055027 (2010)
P. Reimann and M. Kastner
Equilibration of isolated macroscopic quantum systems
New J. Phys., in press
Last modified on 2012-03-14