Statistics of Stochastic Entropy for Recorded Transitions between ENSO States.

We analyze the transitions between established phases of the El Niño Southern Oscillation (ENSO) by surveying the daily data of the southern oscillation index from an entropic viewpoint using the framework of stochastic statistical physics. We evaluate the variation of entropy produced due to each recorded path of that index during each transition as well as taking only into consideration the beginning and the end of the change between phases and verified both integral fluctuation relations. The statistical results show that these entropy variations have not been extreme entropic events; only the transition between the strong 1999-2000 La Niña to the moderate 2002-2003 El Niño is at the edge of being so. With that, the present work opens a long and winding avenue of research over the application of stochastic statistical physics to climate dynamics.

Antivax movement and epidemic spreading in the era of social networks: Nonmonotonic effects, bistability, and network segregation.

In this work, we address a multicoupled dynamics on complex networks with tunable structural segregation. Specifically, we work on a networked epidemic spreading under a vaccination campaign with agents in favor and against the vaccine. Our results show that such coupled dynamics exhibits a myriad of phenomena such as nonequilibrium transitions accompanied by bistability. Besides we observe the emergence of an intermediate optimal segregation level where the community structure enhances negative opinions over vaccination but counterintuitively hinders-rather than favoring-the global disease spreading. Thus our results hint vaccination campaigns should avoid policies that end up segregating excessively antivaccine groups so that they effectively work as echo chambers in which individuals look to confirmation without jeopardizing the safety of the whole population.

Negative correlations can play a positive role in disordered quantum walks.

We investigate the emerging properties of quantum walks with temporal disorder engineered from a binary Markov chain with tailored correlation, C, and disorder strength, r. We show that when the disorder is weak-[Formula: see text]-the introduction of negative correlation leads to a counter-intuitive higher production of spin-lattice entanglement entropy, [Formula: see text], than the setting with positive correlation, that is [Formula: see text]. These results show that negatively correlated disorder plays a more important role in quantum entanglement than it has been assumed in the literature.

Optimal dispersal in ecological dynamics with Allee effect in metapopulations.

We introduce a minimal agent-based model to understand the effects of the interplay between dispersal and geometric constraints in metapopulation dynamics under the Allee Effect. The model, which does not impose nonlinear birth and death rates, is studied both analytically and numerically. Our results indicate the existence of a survival-extinction boundary with monotonic behavior for weak spatial constraints and a nonmonotonic behavior for strong spatial constraints so that there is an optimal dispersal that maximizes the survival probability. Such optimal dispersal has empirical support from recent experiments with engineered bacteria.

Intraday seasonalities and nonstationarity of trading volume in financial markets: Collective features.

Employing Random Matrix Theory and Principal Component Analysis techniques, we enlarge our work on the individual and cross-sectional intraday statistical properties of trading volume in financial markets to the study of collective intraday features of that financial observable. Our data consist of the trading volume of the Dow Jones Industrial Average Index components spanning the years between 2003 and 2014. Computing the intraday time dependent correlation matrices and their spectrum of eigenvalues, we show there is a mode ruling the collective behaviour of the trading volume of these stocks whereas the remaining eigenvalues are within the bounds established by random matrix theory, except the second largest eigenvalue which is robustly above the upper bound limit at the opening and slightly above it during the morning-afternoon transition. Taking into account that for price fluctuations it was reported the existence of at least seven significant eigenvalues-and that its autocorrelation function is close to white noise for highly liquid stocks whereas for the trading volume it lasts significantly for more than 2 hours -, our finding goes against any expectation based on those features, even when we take into account the Epps effect. In addition, the weight of the trading volume collective mode is intraday dependent; its value increases as the trading session advances with its eigenversor approaching the uniform vector as well, which corresponds to a soar in the behavioural homogeneity. With respect to the nonstationarity of the collective features of the trading volume we observe that after the financial crisis of 2008 the coherence function shows the emergence of an upset profile with large fluctuations from that year on, a property that concurs with the modification of the average trading volume profile we noted in our previous individual analysis.

Macroscopic violation of the law of heat conduction.

We analyze a model describing an anharmonic macroscopic chain in contact with general reservoirs that follow the Lévy-Itô theorem on the Gaussian-Poissonian decomposition of the measure. We do so by considering a perturbative approach to compute the heat flux and the (canonical) temperature profile when the system reaches the steady state. This approach allows observing a macroscopic violation of the law of the heat conduction equivalent to that found for small (N=2) systems in contact with general reservoirs, which conveys the ascendency of the nature of the reservoirs over the size of the system.

Intraday Seasonalities and Nonstationarity of Trading Volume in Financial Markets: Individual and Cross-Sectional Features.

We study the intraday behaviour of the statistical moments of the trading volume of the blue chip equities that composed the Dow Jones Industrial Average index between 2003 and 2014. By splitting that time interval into semesters, we provide a quantitative account of the nonstationary nature of the intraday statistical properties as well. Explicitly, we prove the well-known ∪-shape exhibited by the average trading volume-as well as the volatility of the price fluctuations-experienced a significant change from 2008 (the year of the "subprime" financial crisis) onwards. That has resulted in a faster relaxation after the market opening and relates to a consistent decrease in the convexity of the average trading volume intraday profile. Simultaneously, the last part of the session has become steeper as well, a modification that is likely to have been triggered by the new short-selling rules that were introduced in 2007 by the Securities and Exchange Commission. The combination of both results reveals that the ∪ has been turning into a ⊔. Additionally, the analysis of higher-order cumulants-namely the skewness and the kurtosis-shows that the morning and the afternoon parts of the trading session are each clearly associated with different statistical features and hence dynamical rules. Concretely, we claim that the large initial trading volume is due to wayward stocks whereas the large volume during the last part of the session hinges on a cohesive increase of the trading volume. That dissimilarity between the two parts of the trading session is stressed in periods of higher uproar in the market.

Superexponential fluctuation relation for dichotomous work reservoir systems.

This paper introduces an analytical description of the probability density function of the dissipated and injected powers p(j_{dis}) and p(j_{inj}), respectively, in a paradigmatic nonequilibrium damped system in contact with a work reservoir that is analytically represented by telegraph noise and to which one can assign an effective temperature. This approach is able to overcome the well-known impossibility of obtaining closed solutions to steady-state distributions of this system and allows determining a superexponential fluctuation relation of the injected power, which is not even asymptotically exponential as for (shot-noise) Poissonian reservoirs. In the white-noise limit, that relation converges to the exponential formula that is standard in thermal systems; however, the distribution of the injected power remains quite different from that of the latter instance. Surprisingly, it is actually shown that a Gaussian distribution, which is archetypal of thermal systems, for the injected power can be achievable only for athermal reservoirs of this kind.

Thermostatistics of a damped bimodal particle.

We study the thermostatistics of a damped bimodal particle, i.e., a particle of mass m subject to a work reservoir that is analytically represented by the telegraph noise. Because of the colored nature of the noise, it does not fit the Lévy-Itô class of stochastic processes, making this system an instance of a nonequilibrium system in contact with a non-Gaussian external reservoir. We obtain the statistical description of the position and velocity, namely in the stationary state, as well as the (time-dependent) statistics of the energy fluxes in the system considering no constraints on the telegraph noise features. With that result we are able to give an account of the statistical properties of the large deviations of the injected and dissipated power that can change from sub-Gaussianity to super-Gaussianity depending on the color of the noise. By properly defining an effective temperature for this system, T, we are capable of obtaining an equivalent entropy production-exchange rate equal to the ratio between the dissipation of the medium, γ, and the mass of the particle, m, a relation that concurs with the case of a standard thermal reservoir at temperature, T=T.

Thermostatistics of small nonlinear systems: Gaussian thermal bath.

We discuss the statistical properties of small mechanothermodynamic systems (one- and two-particle cases) subject to nonlinear coupling and in contact with standard Gaussian reservoirs. We use a method that applies averages in the Laplace-Fourier space, which relates to a generalization of the final-value theorem. The key advantage of this method lies in the possibility of eschewing the explicit computation of the propagator, traditionally required in alternative methods like path integral calculations, which is hardly obtainable in the majority of the cases. For one-particle equilibrium systems we are able to compute the instantaneous (equilibrium) probability density functions of injected and dissipated power as well as the respective large deviation functions. Our thorough calculations explicitly show that for such models nonlinearities are irrelevant in the long-term statistics, which preserve the exact same values as computed for linear cases. Actually, we verify that the thermostatistical effect of the nonlinearities is constricted to the transient towards equilibrium, since it affects the average total energy of the system. For the two-particle system we consider each element in contact with a heat reservoir, at different temperatures, and focus on the problem of heat flux between them. Contrarily to the one-particle case, in this steady state nonequilibrium model we prove that the heat flux probability density function reflects the existence of nonlinearities in the system. An important consequence of that it is the temperature dependence of the conductance, which is unobserved in linear(harmonic) models. Our results are complemented by fluctuation relations for the injected power (equilibrium case) and heat flux (nonequilibrium case).

Components of multifractality in the central England temperature anomaly series.

We study the multifractal nature of the Central England Temperature (CET) anomaly, a time series that spans more than 200 years. The data are analyzed in two ways: as a single set and by using a sliding window of 11 years. In both cases, we quantify the width of the multifractal spectrum as well as its components, which are defined by the deviations from the Gaussian distribution and the dependence between measurements. The results of the first approach show that the key contribution to the multifractal structure comes from the dynamical dependencies, mainly weak ones, followed by a residual contribution of the deviations from the Gaussian. The sliding window approach indicates that the peaks in the evolution of the non-Gaussian contribution occur almost at the same dates associated with climate changes that were determined in previous works using component analysis methods. Moreover, the strong non-Gaussian contribution from the 1960 s onwards is in agreement with global results recently presented.

Role of the nature of noise in the thermal conductance of mechanical systems.

Focusing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the Lévy-Itô nature of the noise in the thermal conductance. For white noises, we prove that the Lévy-Itô composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a nonequilibrium linearly coupled chain, which signals the independence of mechanical and thermodynamical properties. In contrast, for the nonlinearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role.

Minding impacting events in a model of stochastic variance.

We introduce a generalization of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold, , and another one when the local standard deviation outnumbers . In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterized by large values of the Hurst exponent (H>0.8), which are ubiquitous features in complex systems.

Effect of platykurtic and leptokurtic distributions in the random-field Ising model: mean-field approach.

The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose value is in accordance with a generic distribution that bears platykurtic and leptokurtic distributions depending on a single parameter tau<3 to each site. For tau<5/3, such distributions, which are basically Student-t and r distribution extended for all plausible real degrees of freedom, present a finite standard deviation, if not the distribution has got the same asymptotic power-law behavior as a alpha-stable Lévy distribution with alpha=(3-tau)/(tau-1). For every value of tau, at specific temperature and width of the distribution, the system undergoes a continuous phase transition. Strikingly, we impart the emergence of an inflexion point in the temperature-PDF width phase diagrams for distributions broader than the Cauchy-Lorentz (tau=2) which is accompanied with a divergent free energy per spin (at zero temperature).

Effectiveness of the Kozachenko-Leonenko estimator for generalized entropic forms.

In this Brief Report we discuss the effectiveness of the Kozachenko-Leonenko entropy estimator when generalized to cope with entropic forms customarily applied to study systems evincing asymptotic scale invariance and dependence (either of linear or nonlinear kind). We show that when the variables are independently and identically distributed the estimator is only valuable along the whole domain if the data follow the uniform distribution, whereas for other distributions the estimator is only effectual in the limit of the Boltzmann-Gibbs-Shanon entropic form. We also analyze the influence of the dependence (linear and nonlinear) between variables on the accuracy of the estimator between variables. As expected in the last case the estimator loses efficiency for the Boltzmann-Gibbs-Shanon entropic form as well.