Generalized entropies in quantum and classical statistical theories

Abstract

We study a version of the generalized (h, φ)-entropies, introduced by Salicrú et al, for a wide family of probabilistic models that includes quantum and classical statistical theories as particular cases. We extend previous works by exploring how to define (h, φ)-entropies in infinite dimensional models.

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

“…Notice that, in the present application of the S q entropies, the particular value q = 2 is an inevitable consequence of the structure of the inner product in Hilbert space, which provides a natural way to assess the distinguishability between quantum pure states. The problem considered in the present work illustrates the fact that non-standard or generalized entropies [24,25] arise naturally in the study of physical systems or processes.…”

Quantum systems in and out of equilibrium

“…A third group covers rather different topics, including information entropies, atomic physics or quantum computation. Zozor and coworkers [11] study generalized entropies in quantum and classical statistical theories; Toranzo and coworkers [12] determine the exact values of the Rényi uncertainty measures of D-dimensional harmonic systems; Ramsak et al [13] consider exactly solvable manipulation of spinorbit qubits confined in a moving harmonic trap and in the presence of the time dependent Rashba interaction; lastly, Kastner and Uhrich [14] generalise a former result to prove that special observables exist for which measurement backaction is of no concern when measuring temporal correlations.…”

Solutions for the MaxEnt problem with symmetry constraints

“…Von Neumann's entropy can be considered as a natural non-commutative generalization of Shannon's entropy [25,26]. While in this work we use the Shannon and von Neumann entropies, it is important to remark that there exist other entropic quantities that find many applications in diverse fields of research [25,27,28,29,30,31,32,33,34,35]. In the case that the available information is given by the mean value of some set of observables, the probability distribution can be obtained using Lagrange multipliers.…”