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Open AccessArticle

Quantum Features of Macroscopic Fields: Entropy and Dynamics

International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland
Entropy 2019, 21(7), 705;
Received: 12 April 2019 / Revised: 12 May 2019 / Accepted: 17 July 2019 / Published: 18 July 2019
(This article belongs to the Special Issue Quantum Entropies and Complexity)
PDF [269 KB, uploaded 22 July 2019]


Macroscopic fields such as electromagnetic, magnetohydrodynamic, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of the field combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equation for the reduced state of the field is obtained by reduction of the generalized quasi-free dynamical semigroups describing irreversible evolution of bosonic quantum field and the definition of entropy for the reduced state of the field follows from the von Neumann entropy of quantum field states. The presented formalism can be applied, for example, to superradiance phenomena and allows unifying the Mueller and Jones calculi in polarization optics. View Full-Text
Keywords: classical field theory; quantum open systems; von Neumann entropy; Mueller Jones calculi classical field theory; quantum open systems; von Neumann entropy; Mueller Jones calculi
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 (CC BY 4.0).

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Alicki, R. Quantum Features of Macroscopic Fields: Entropy and Dynamics. Entropy 2019, 21, 705.

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