Searcharxiv⌕ Search

arXiv subjects

P. Grigolini

Publications and source records attributed to P. Grigolini.

31 records · Page 2Linked to original sources
arXiv2002

Non-extensive diffusion entropy analysis: non-stationarity in teen birth phenomena

A complex process is often a balance between non-stationary and stationary components. We show how the non-extensive Tsallis q-entropy indicator may be interpreted as a measure of non-stationarity in time series. This is done by applying the non-extensive entropy formalism to the Diffusion Entropy Analysis (DEA). We apply the analysis to the study of the teen birth phenomenon. We find that the unmarried teen births are strongly influenced by social processes with memory. This memory is related to the strength of the non-stationary component of the signal and is more intense than that in the married teen time series. By using the wavelet multiresolution analysis we attempt to give a social interpretation of this effect.

cond-mat.stat-mech↗
arXiv2002

Entropic Analysis of non-Stationary Sequences

The aim of this paper is to shed light on the analysis of non-stationary time series by means of the method of diffusion entropy. For this purpose, we first study the case when infinitely many time series, as different realizations of the same dynamic process, are available, so as to adopt the Gibbs ensemble perspective. We solve the problem of establishing under which conditions scaling emerges from within this perspective. Then, we study the more challenging problem of creating a diffusion process from only one single (non-stationary) time series. The conversion of this single sequence into many diffusional trajectories is equivalent to creating a non-Gibbsian ensemble. However, adopting a probabilistic approach to evaluate the contribution of any system of this non-Gibbsian ensemble, and using for it the theoretical Gibbsian prescription of the earlier case, we find a recipe that fits accurately the numerical results. With the help of this recipe we show that nonstationary time series produce either anomalous scaling with ordinary statistics or ordinary scaling with anomalous statistics. From this recipe we also derive an attractive way to explain the entropy time evolution, as resulting from two distinct uncertainty sources, the lack of information on the trajectory initial condition, and the lack of control on random trajectories.

cond-mat.stat-mech↗
arXiv2002

Compression and diffusion: a joint approach to detect complexity

The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called Compression Algorithm Sensitive To Regularity (CASToRe), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work.

cond-mat↗
arXiv2001

Strange kinetics: conflict between density and trajectory description

We study a process of anomalous diffusion, based on intermittent velocity fluctuations, and we show that its scaling depends on whether we observe the motion of many independent trajectories or that of a Liouville-like equation driven density. The reason for this discrepancy seems to be that the Liouville-like equation is unable to reproduce the multi-scaling properties emerging from trajectory dynamics. We argue that this conflict between density and trajectory might help us to define the uncertain border between dynamics and thermodynamics, and that between quantum and classical physics as well.

cond-mat.stat-mech↗
arXiv2001

Aging Induced Multifractality

We show that the dynamic approach to Lévy statistics is characterized by aging and multifractality, induced by an ultra-slow transition to anomalous scaling. We argue that these aspects make it a protoptype of complex systems.

cond-mat.stat-mech↗
arXiv2001

Facing Non-Stationary Conditions with a New Indicator of Entropy Increase: The Cassandra Algorithm

We address the problem of detecting non-stationary effects in time series (in particular fractal time series) by means of the Diffusion Entropy Method (DEM). This means that the experimental sequence under study, of size $N$, is explored with a window of size $L << N$. The DEM makes a wise use of the statistical information available and, consequently, in spite of the modest size of the window used, does succeed in revealing local statistical properties, and it shows how they change upon moving the windows along the experimental sequence. The method is expected to work also to predict catastrophic events before their occurrence.

cond-mat.stat-mech↗
arXiv2001

Memory beyond memory in heart beating: an efficient way to detect pathological conditions

We study the long-range correlations of heartbeat fluctuations with the method of diffusion entropy. We show that this method of analysis yields a scaling parameter $δ$ that apparently conflicts with the direct evaluation of the distribution of times of sojourn in states with a given heartbeat frequency. The strength of the memory responsible for this discrepancy is given by a parameter $ε^{2}$, which is derived from real data. The distribution of patients in the ($δ$, $ε^{2}$)-plane yields a neat separation of the healthy from the congestive heart failure subjects.

cond-mat.stat-mech↗
arXiv2000

Canonical and non-canonical equilibrium distribution

We address the problem of the dynamical foundation of non-canonical equilibrium. We consider, as a source of divergence from ordinary statistical mechanics, the breakdown of the condition of time scale separation between microscopic and macroscopic dynamics. We show that this breakdown has the effect of producing a significant deviation from the canonical prescription. We also show that, while the canonical equilibrium can be reached with no apparent dependence on dynamics, the specific form of non-canonical equilibrium is, in fact, determined by dynamics. We consider the special case where the thermal reservoir driving the system of interest to equilibrium is a generator of intermittent fluctuations. We assess the form of the non-canonical equilibrium reached by the system in this case. Using both theoretical and numerical arguments we demonstrate that Levy statistics are the best description of the dynamics and that the Levy distribution is the correct basin of attraction. We also show that the correct path to non-canonical equilibrium by means of strictly thermodynamic arguments has not yet been found, and that further research has to be done to establish a connection between dynamics and thermodynamics.

cond-mat.stat-mech↗
arXiv1999

The non-extensive version of the Kolmogorov-Sinai entropy at work

We address the problem of applying the Kolmogorov-Sinai method of entropic analysis, expressed in a generalized non-extensive form, to the dynamics of the logistic map at the chaotic threshold, which is known to be characterized by a power law rather than exponential sensitivity to initial conditions. The computer treatment is made difficult, if not impossible, by the multifractal nature of the natural invariant distribution: Thus the statistical average is carried out on the power index. The resulting entropy time evolution becomes a smooth and linear function of time with the non-extensive index Q < 1 prescribed by the heuristic arguments of earlier work, thereby showing how to make the correct entropic prediction in the spirit of the single-trajectory approach of Kolmogorov.

cond-mat↗
arXiv1999

Stochastic versus dynamic approach to Levy statistics in the presence of an external perturbation

We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regime. When the latter regime applies, the system is attracted by the basin of either Gauss or Levy statistics according to whether the fluctuation correlation function is integrable or not. We analyze with a numerical calculation the border between the two basins of attraction.

cond-mat.stat-mech↗
arXiv1999

A Fluctuation-Dissipation Process without Time Scale

We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically, with a good agreement between theory and numerical treatment. As a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution. The distribution tails are truncated, the distribution border is signalled by sharp peaks and, in the weak dissipation limit, the central distribution body becomes identical to a truncated Levy distribution.

cond-mat.stat-mech↗
arXiv1998

Fractional Calculus as a Macroscopic Manifestation of Randomness

We generalize the method of Van Hove so as to deal with the case of non-ordinary statistical mechanics, that being phenomena with no time-scale separation. We show that in the case of ordinary statistical mechanics, even if the adoption of the Van Hove method imposes randomness upon Hamiltonian dynamics, the resulting statistical process is described using normal calculus techniques. On the other hand, in the case where there is no time-scale separation, this generalized version of Van Hove's method not only imposes randomness upon the microscopic dynamics, but it also transmits randomness to the macroscopic level. As a result, the correct description of macroscopic dynamics has to be expressed in terms of the fractional calculus.

cond-mat↗