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Quantum Central Limit Theorems, Emergence of Classicality and Time-dependent Differential Entropy
Version 1
: Received: 7 March 2023 / Approved: 9 March 2023 / Online: 9 March 2023 (09:27:19 CET)
A peer-reviewed article of this Preprint also exists.
Kieu, T.D. Quantum Central Limit Theorems, Emergence of Classicality and Time-Dependent Differential Entropy. Entropy 2023, 25, 600. Kieu, T.D. Quantum Central Limit Theorems, Emergence of Classicality and Time-Dependent Differential Entropy. Entropy 2023, 25, 600.
Abstract
We derive some Quantum Central Limit Theorems for expectation values of macroscopically
coarse-grained observables, which are functions of coarse-grained hermitean operators consisting
of non-commuting variables. Thanks to the hermicity constraints, we obtain positive-definite dis-
tribution for the expectation values of observables. These probability distributions open some
pathway for an emergence of classical behaviours in the limit of in nitely large number of identical
and non-interacting quantum constituents. This is in contradistinction to other mechanisms of
classicality emergence due to environmental decoherence and consistent histories. The probabil-
ity distributions so derived also enable us to evaluate the nontrivial time-dependence of certain
differential entropies.
Keywords
Quantum central limit theorems
Subject
Physical Sciences, Quantum Science and Technology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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