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arXiv:quant-ph/0507218

Can We Believe in a Purely Unitary Quantum Dynamics?

Fedor Herbut

Published Jul 22, 2005• 2 citations
arXivHTMLPDF

Abstract

It is pointed out that the question of a purely unitary quantum dynamics amounts to the question if von Neumann entropy of a dynamically closed quantum system is preserved in evolution.
DOI
10.48550/arxiv.quant-ph/0507218

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We propose a generalization of the quantum entropy introduced by Wigner and von Neumann [Z. Phys. 57, 30 (1929)10.1007/BF01339852]. Our generalization is applicable to both quantum pure states and mixed states. When the dimension N of the Hilbert space is large, this generalized Wigner-von Neumann (GWvN) entropy becomes independent of the choices of basis and is asymptotically equal to lnN in the sense of typicality. The dynamic evolution of our entropy is also typical, and is reminiscent of quantum H theorem proved by von Neumann. For a composite system, the GWvN entropy is typically additive; for the microcanonical ensemble, it is equivalent to the Boltzmann entropy; and for a system entangled with environment, it is consistent with the familiar von Neumann entropy, which is zero for pure states. In addition, the GWvN entropy can be used to derive the Gibbs ensemble.
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