New Trends in Statistical Physics of Complex Systems

A topical research activity in statistical physics concerns the study of complex and disordered systems. Generally, these systems are characterized by an elevated level of interconnection and interaction between the parts so that they give rise to a rich structure in the phase space that self-organizes under the control of internal non-linear dynamics. These emergent collective dynamics confer new behaviours to the whole system that are no longer the direct consequence of the properties of the single parts, but rather characterize the whole system as a new entity with its own features, giving rise to the birth of new phenomenologies. As is highlighted in this collection of papers, the methodologies of statistical physics have become very promising in understanding these new phenomena. This volume groups together 12 research works showing the use of typical tools developed within the framework of statistical mechanics, in non-linear kinetic and information geometry, to investigate emerging features in complex physical and physical-like systems. A topical research activity in statistical physics concerns the study of complex and disordered systems. Generally, these systems are characterized by an elevated level of interconnection and interaction between the parts so that they give rise to a rich structure in the phase space that self-organizes under the control of internal non-linear dynamics. These emergent collective dynamics confer new behaviours to the whole system that are no longer the direct consequence of the properties of the single parts, but rather characterize the whole system as a new entity with its own features, giving rise to the birth of new phenomenologies. As is highlighted in this collection of papers, the methodologies of statistical physics have become very promising in understanding these new phenomena. This volume groups together 12 research works showing the use of typical tools developed within the framework of statistical mechanics, in non-linear kinetic and information geometry, to investigate emerging features in complex physical and physical-like systems

On the Kaniadakis distributions applied in statistical physics and natural sciences

Constitutive relations are fundamental and essential to characterize physical systems. By utilizing the $\kappa$-deformed functions, some constitutive relations are generalized. We here show some applications of the Kaniadakis distributions based on the inverse hyperbolic sine function to some topics belonging to the realm of statistical physics and natural science.Comment: 14 pages, 2 figures, submitted to Entrop

Advantages of qq-logarithm representation over qq-exponential representation from the sense of scale and shift on nonlinear systems

Addition and subtraction of observed values can be computed under the obvious and implicit assumption that the scale unit of measurement should be the same for all arguments, which is valid even for any nonlinear systems. This paper starts with the distinction between exponential and non-exponential family in the sense of the scale unit of measurement. In the simplest nonlinear model ${dy}/{dx}=y^{q}$, it is shown how typical effects such as rescaling and shift emerge in the nonlinear systems and affect observed data. Based on the present results, the two representations, namely the $q$-exponential and the $q$-logarithm ones, are proposed. The former is for rescaling, the latter for unified understanding with a fixed scale unit. As applications of these representations, the corresponding entropy and the general probability expression for unified understanding with a fixed scale unit are presented. For the theoretical study of nonlinear systems, $q$-logarithm representation is shown to have significant advantages over $q$-exponential representation.Comment: 13 pages, 3 figure

The Kinetics of Sorption–Desorption Phenomena: Local and Non-Local Kinetic Equations

The kinetics of adsorption phenomena are investigated in terms of local and non-local kinetic equations of the Langmuir type. The sample is assumed in the shape of a slab, limited by two homogeneous planar-parallel surfaces, in such a manner that the problem can be considered one-dimensional. The local kinetic equations in time are analyzed when both saturation and nonsaturation regimes are considered. These effects result from an extra dependence of the adsorption coefficient on the density of adsorbed particles, which implies the consideration of nonlinear balance equations. Non-local kinetic equations, arising from the existence of a time delay characterizing a type of reaction occurring between a bulk particle and the surface, are analyzed and show the existence of adsorption effects accompanied by temporal oscillations

The k-statistics approach to epidemiology

A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced $\kappa$-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of $\kappa$-statistics in fitting empirical data. In this paper, we use $\kappa$-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived $\kappa$-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the $\kappa$-Weibull model has universal features.Comment: 15 pages, 1 table, 5 figure

Quantum Computation and Information: Multi-Particle Aspects

This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers