A Generalized Statistical Complexity Measure: Applications to Quantum Systems

A two-parameter family of complexity measures $\tilde{C}^{(\alpha,\beta)}$ based on the R\'enyi entropies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous version of the LMC complexity, which is recovered for $\alpha=1$ and $\beta=2$. These complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system. When one of the parameters, $\alpha$ or $\beta$, goes to infinity, one of the global factors becomes a local factor. For this special case, the complexity is calculated on different quantum systems: H-atom, harmonic oscillator and square well.Comment: 15 pages, 3 figure

SŰRŰSÉG FUNKCIONÁL ÉS SŰRŰSÉGMÁTRIX ELMÉLETEK = DENSITY FUNCTIONAL AND DENSITY MATRIX THEORIES

Napjainkban az elektronszerkezet-számítások többnyire a sűrűségfunkcionál elmélet Kohn-Sham-egyenleteinek megoldásával történnek. Ennek az az oka, hogy nem ismerjük a kinetikus energiafunkcionált (mint a sűrűség funkcionálját). A kinetikus energiát a pályak funkcionáljaként ismerjük csak. Általában annyi Kohn-Sham-egyenletet kell megoldani, ahány elektron van a vizsgált rendszerben. A kinetikus energiafunkcionál ismeretében viszont elegendő mindig csak egyetlen egyenletet, az ú.n. Euler-egyenletet megoldani akárhány elektron is van jelen. Egy ilyen pálya-független módszer lehetővé teszi igen nagy rendszerek tárgyalását is. Ezért van nagy jelentőségük az ilyen irányú kutatásoknak. A pályázat legfontosabb eredménye, hogy sikerült jelentős előrehaladást elérni a kinetikus energia több mint 80 éve megoldatlan problémájában: A Nagy-March differenciális viriáltétel sokaságra történő általánosításából elsőrendű differenciálegyenletet vezettünk le a sokaság kinetikus energia funkcionálderiváltjára gömbszimmetrikus rendszerekre. Az egyenlet megoldásának egy speciális esete megadja az eredeti kinetikus energiát. Ez az eredeti probléma egzakt megoldását jelenti, de csak gömbszimmetrikus esetben. További fontos eredmények: egzakt tételeket, relációkat vezettünk le a sűrűségmátrix funkcionál elméletben. Összefüggést találtunk, a Fisher-informáciÓ, a Rényi-információ és a kinetikus energia között. | Nowadays, electron structure calculations are mainly done by the solution of the Kohn-Sham equations of the density functional theory. The reason is that the kinetic energy functional (as a functional of the density) is unknown. The kinetic energy is known only as a functional of the orbitals. One has to solve as many Kohn-Sham equations as the number of electrons. In the knowledge of the kinetic energy functional, one always has to solve a single equation, the so called Euler equation independently of the number of electrons in the system. Such an orbital-free method makes it possible to treat very large systems. That is why studies in this direction are very important. An important progress has been achieved in the problem of kinetic energy unsolved more than 80 years. The differential virial theorem of Nagy and March is generalized for ensembles. A first-order differential equation for the functional derivative of the ensemble non-interacting kinetic energy functional has been derived. A special case of the solution of this equation gives the original non-interacting kinetic energy. This provides the exact solution of the original problem but only for spherically symmetric case. Further important results: exact theorems and relations have been derived in the density matrix functional theory. Relations have been obtained between the Fisher information, the Rényi information and the kinetic energy

Characterization of autoregressive processes using entropic quantifiers

The aim of the contribution is to introduce a novel information plane, the causal-amplitude informational plane. As previous works seems to indicate, Bandt and Pompe methodology for estimating entropy does not allow to distinguish between probability distributions which could be fundamental for simulation or for probability analysis purposes. Once a time series is identified as stochastic by the causal complexity-entropy informational plane, the novel causal-amplitude gives a deeper understanding of the time series, quantifying both, the autocorrelation strength and the probability distribution of the data extracted from the generating processes. Two examples are presented, one from climate change model and the other from financial markets.Fil: Traversaro Varela, Francisco. Instituto Tecnológico de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Redelico, Francisco Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Hospital Italiano; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentin

Wavelet-Based Multiscale Intermittency Analysis: The Effect of Deformation

Intermittency represents a certain form of heterogeneous behavior that has interest in diverse fields of application, particularly regarding the characterization of system dynamics and for risk assessment. Given its intrinsic location-scale-dependent nature, wavelets constitute a useful functional tool for technical analysis of intermittency. Deformation of the support may induce complex structural changes in a signal. In this paper, we study the effect of deformation on intermittency. Specifically, we analyze the interscale transfer of energy and its implications on different wavelet-based intermittency indicators, depending on whether the signal corresponds to a ‘level’- or a ‘flow’-type physical magnitude. Further, we evaluate the effect of deformation on the interscale distribution of energy in terms of generalized entropy and complexity measures. For illustration, various contrasting scenarios are considered based on simulation, as well as two segments corresponding to different regimes in a real seismic series before and after a significant earthquake.PID2021-128077NB-I00 and PGC2018-098860- B-I00MCIN/AEI/10.13039/501100011033/ERDF A way of making Europe, EUCEX2020-001105-M funded by MCIN/AEI/10.13039/50110001103