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Entropic Characterization of Quantum States with Maximal Evolution under Given Energy Constraints

Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Av. Medina Allende s/n, Ciudad Universitaria, Córdoba X5000HUA, Argentina
Instituto de Física Enrique Gaviola (IFEG), Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina (CONICET), Córdoba X5000HUA, Argentina
Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, Ciudad de México, Mexico
CeBio y Departamento de Ciencias Básicas, Universidad Nacional del Noroeste de la Prov. de Buenos Aires, UNNOBA, CONICET, Roque Saenz Peña 456, Junín B6000, Argentina
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2019, 21(8), 770;
Received: 24 May 2019 / Revised: 29 July 2019 / Accepted: 2 August 2019 / Published: 7 August 2019
PDF [1610 KB, uploaded 8 August 2019]


A measure D [ t 1 , t 2 ] for the amount of dynamical evolution exhibited by a quantum system during a time interval [ t 1 , t 2 ] is defined in terms of how distinguishable from each other are, on average, the states of the system at different times. We investigate some properties of the measure D showing that, for increasing values of the interval’s duration, the measure quickly reaches an asymptotic value given by the linear entropy of the energy distribution associated with the system’s (pure) quantum state. This leads to the formulation of an entropic variational problem characterizing the quantum states that exhibit the largest amount of dynamical evolution under energy constraints given by the expectation value of the energy. View Full-Text
Keywords: quantum evolution; distinguishability of quantum states; maximum entropy quantum evolution; distinguishability of quantum states; maximum entropy

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Majtey, A.P.; Valdés-Hernández, A.; Maglione, C.G.; Plastino, A.R. Entropic Characterization of Quantum States with Maximal Evolution under Given Energy Constraints. Entropy 2019, 21, 770.

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