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The notion of entropy is ubiquitous both in natural and social sciences. In the last two decades, a considerable effort has been devoted to the study of new entropic forms, which generalize the standard Boltzmann-Gibbs (BC) entropy and could be [...]texto impreso
Carrasco, José A. ; Finkel Morgenstern, Federico ; González López, Artemio ; Rodríguez González, Miguel Ángel ; Tempesta, Piergiulio | American Physical Society | 2016-07-01We introduce a general class of su(1 / 1) supersymmetric spin chains with long-range interactions which includes as particular cases the su (1 / 1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this clas[...]texto impreso
Carrasco, José A. ; Finkel Morgenstern, Federico ; González López, Artemio ; Rodríguez González, Miguel Ángel ; Tempesta, Piergiulio | American Physical Society | 2016-06-01We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of [...]texto impreso
Carrasco, J. A. ; Finkel Morgenstern, Federico ; González López, Artemio ; Tempesta, Piergiulio | Nature Publishing Group | 2017-09-11The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of [...]texto impreso
We shall prove that the celebrated Renyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropie[...]texto impreso
Carrasco, José A. ; Finkel Morgenstern, Federico ; González López, Artemio ; Rodríguez González, Miguel Ángel ; Tempesta, Piergiulio | IOP Publishing | 2016-03We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced [...]texto impreso
The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composa[...]texto impreso
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the c[...]texto impreso
In the context of the theory of symplectic-Haantjes manifolds, we construct the Haantjes structures of generalized Stackel systems and, as a particular case, of the quasi-bi-Hamiltonian systems. As an application, we recover the Haantjes manifol[...]texto impreso
We define the class of multivariate group entropies as a novel set of information-theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality class of c[...]texto impreso
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for a la[...]texto impreso
A multi-parametric version of the nonadditive entropy S_q is introduced. This new entropic form, denoted by S_a,b,r, possesses many interesting statistical properties, and it reduces to the entropy S_q for b=0, a=r:=1?q (hence Boltzmann–Gibbs en[...]texto impreso
Ibort, A. ; Marmo, G. ; Rodríguez González, Miguel Ángel ; Tempesta, Piergiulio | Springer Heidelberg | 2019-10We present an algebraic formulation of the notion of integrability of dynamical systems, based on a nilpotency property of its flow: It can be explicitly described as a polynomial on its evolution parameter. Such a property is established in a p[...]texto impreso
Sicuro, Gabriele ; Tempesta, Piergiulio ; Rodriguez, Antonio ; Tsallis, Constantino | Elsevier Masson | 2015-12We introduce three deformations, called ?-, ?-, and ? deformation respectively, of a N-body probabilistic model, first proposed by Rodriguez et al. (2008), having q-Gaussians as N ? ? limiting probability distributions. The proposed ?- and ?-def[...]texto impreso
We present a message-passing based parallel version of the Space Saving algorithm designed to solve the k-majority problem. The algorithm determines in parallel frequent items, i.e., those whose frequency is greater than a given threshold, and i[...]
