Concept of the Statistical Ensemble

M. I. Gorenstein

김재영

I examined the Statistical Ensemble Interpretation (SEI) of quantum mechanics. Historical reappraisal of Max Born's statistical interpretation shows precisely how Born used the concept of the probability. After investigating the so-called Ensemble Interpretation proposed by Albert Einstein based on ...

Thomas A. Brody

V.A. Kasimov

The current situation of the search for the essence of space-time relations reminds the early history of the search for the essence of phlogiston, which was resolved by the statistical theory of Gibbs ensembles, the definition of thermodynamic concepts and, in particular, the concept of temperature as the average kinetic energy in the ensemble. Thermodynamics has found its justification in statistical physics but space-time relationships of the macrocosm it is possible that it will find its rationale in the inevitable processes of condensation and localization in the environment of prameter and averaging the probabilistic parameters of the microcosm in the description of these processes.

Thomas A. Brody

Yinxiù Zhan, Matteo G. A. Paris

The main purpose of this tutorial is to elucidate in details what should be meant by ensemble of states in quantum mechanics, and to properly address the problem of discriminating, exactly or approximately, two different ensembles. To this aim, we review the notion and the definition of quantum ensemble as well as its relationships with the concept of statistical operator in quantum mechanics. We point out the implicit assumptions contained in introducing a correspondence between quantum ensembles and the corresponding single-particle statistical operator, and discuss some issues arising when these assumptions are not satisfied. We review some subtleties leading to apparent paradoxes, and illustrate the role of approximate quantum cloning. In particular, we review some examples of practical interest where different (but equivalent) preparations of a quantum system, i.e. different ensembles corresponding to the same single-particle statistical operator, may be successfully discriminated exploiting multiparticle correlations, or some a priori knowledge about the number of particles in the ensemble.