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Communications in Nonlinear Science and Numerical Simulation

Entropy analysis of systems exhibiting negative probabilities

J. A. Tenreiro Machado

Published Dec 1, 2015• 9 citations
Publisher
DOI
10.1016/j.cnsns.2015.11.022

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In a previous essay I argued that quantum chaos cannot be exhibited in models of quantum systems within von Neumann's mathematical framework for quantum mechanics, and that it can be exhibited in models within Dirac's formal framework. In this essay, the negative thesis concerning von Neumann's framework is elaborated further by extending it to the case of Hamiltonian operators having a continuous spectrum. The positive thesis concerning Dirac's formal framework is also elaborated further by constructing a chaotic model of an open quantum system in which an entropy measure is shown to approach its maximum value as time goes to infinity. Having such an entropy measure is a characteristic that is closely connected to chaotic behavior in phase space models of classical systems.