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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (30 April 2018) | Viewed by 54743

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Dr. Antonio M. Scarfone

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Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche (ISC-CNR), c/o DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Turin, Italy
Interests: nonextensive statistical mechanics; nonlinear fokker-planck equations; geometry information; nonlinear schroedinger equation; quantum groups and quantum algebras; complex systems
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Special Issue Information

Dear Colleagues,

A challenging frontier in statistical physics concerns the study of complex and disordered systems. An interesting aspect of complex systems is the emergence of self-organization, which often drives the system in a metastable configuration, typically far from the thermodynamic limit, where the equilibrium distribution differs significantly from the Boltzmann-Gibbs exponential one.

Complex systems are not necessarily composed of many entities. They can be small systems with few entities but characterized by an elevated level of interconnection and interaction between the parts that exhibit a richer global free-scale dynamic. This gives rise to collective emergent behaviors of the entire system that are no more recognized in the properties and in the behavior of the single individual entities. In this ground, the methods of statistical physics in understanding complex systems have been very promising.

The aim of this Special Issue is to encourage researchers to present original and recent developments on complex and disordered systems and their applications to physical and physical like systems. For instance, applications of the statistical complex systems range from small systems to nano systems, from molecular biology to micromechanics, networks structures and (multi)-fractal phase space to new results in stochastic thermodynamics. Other good examples may be found in economic and social systems.

Prof. Dr. Antonio Maria Scarfone
Guest Editor

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Keywords

generalizations of statistical mechanics
fractional dynamics
non-equilibrium processes
stochastic processes
quantum and small systems
collective phenomena in biological, economic and social systems

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Published Papers (13 papers)

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Editorial

Jump to: Research

4 pages, 164 KiB

Open AccessEditorial

New Trends in Statistical Physics of Complex Systems

by Antonio M. Scarfone

Entropy 2018, 20(12), 906; https://doi.org/10.3390/e20120906 - 27 Nov 2018

Viewed by 2538

Abstract

A challenging frontier in physics concerns the study of complex and disordered systems. [...] Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

Research

Jump to: Editorial

15 pages, 3457 KiB

Open AccessArticle

Study on Bifurcation and Dual Solutions in Natural Convection in a Horizontal Annulus with Rotating Inner Cylinder Using Thermal Immersed Boundary-Lattice Boltzmann Method

by Yikun Wei, Zhengdao Wang, Yuehong Qian and Wenjing Guo

Entropy 2018, 20(10), 733; https://doi.org/10.3390/e20100733 - 25 Sep 2018

Cited by 11 | Viewed by 3345

Abstract

A numerical investigation has been carried out to understand the mechanism of the rotation effect on bifurcation and dual solutions in natural convection within a horizontal annulus. A thermal immersed boundary-lattice Boltzmann method was used to resolve the annular flow domain covered by a Cartesian mesh. The Rayleigh number based on the gap width is fixed at 10⁴. The rotation effect on the natural convection is analyzed by streamlines, isotherms, phase portrait and bifurcation diagram. Our results manifest the existence of three convection patterns in a horizontal annulus with rotating inner cylinder which affect the heat transfer in different ways, and the linear speed (

U_{i}^{*}

) determines the proportion of each convection. Comparison of average Nusselt number versus linear speed for the inner cylinder indicates the existence of the three different mechanisms which drive the convection in a rotation system. The convection pattern caused by rotation reduces the heat transfer efficiency. Our results in phase portraits also reveal the differences among different convection patterns. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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23 pages, 453 KiB

Open AccessArticle

Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking

by Takeshi Ooshida, Susumu Goto and Michio Otsuki

Entropy 2018, 20(8), 565; https://doi.org/10.3390/e20080565 - 2 Aug 2018

Cited by 5 | Viewed by 3995

Abstract

Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as the particles are constantly pushed back by their neighbors. Since this “cage effect” emerges from many-body dynamics involving spatiotemporally correlated motions, the slow diffusion should be understood not simply as a one-body problem but as a part of collective dynamics, described in terms of space–time correlations. Such collective dynamics are illustrated here by calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel, whose subdiffusive behavior is known as the single-file diffusion (SFD). The analytical calculation is formulated in terms of the Lagrangian correlation of density fluctuations. In addition, numerical solutions to the Langevin equation with large but finite interaction potential are studied to clarify the effect of overtaking. In the limiting case of the ideal SFD without overtaking, correlated motion with a diffusively growing length scale is observed. By allowing the particles to overtake each other, the short-range correlation is destroyed, but the long-range weak correlation remains almost intact. These results describe nested space–time structure of cages, whereby smaller cages are enclosed in larger cages with longer lifetimes. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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10 pages, 372 KiB

Open AccessArticle

Information-Length Scaling in a Generalized One-Dimensional Lloyd’s Model

by J. A. Méndez-Bermúdez and R. Aguilar-Sánchez

Entropy 2018, 20(4), 300; https://doi.org/10.3390/e20040300 - 20 Apr 2018

Cited by 2 | Viewed by 3683

Abstract

We perform a detailed numerical study of the localization properties of the eigenfunctions of one-dimensional (1D) tight-binding wires with on-site disorder characterized by long-tailed distributions: For large

ϵ

P (ϵ) \sim 1 / ϵ^{1 + α}

with [...] Read more.

ϵ

P (ϵ) \sim 1 / ϵ^{1 + α}

with

α \in (0, 2]

; where

ϵ

are the on-site random energies. Our model serves as a generalization of 1D Lloyd’s model, which corresponds to

α = 1

. In particular, we demonstrate that the information length

β

of the eigenfunctions follows the scaling law

β = γ x / (1 + γ x)

, with

x = ξ / L

and

γ \equiv γ (α)

. Here,

ξ

is the eigenfunction localization length (that we extract from the scaling of Landauer’s conductance) and L is the wire length. We also report that for

α = 2

the properties of the 1D Anderson model are effectively reproduced. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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16 pages, 12299 KiB

Open AccessArticle

A Mathematical Realization of Entropy through Neutron Slowing Down

by Barry Ganapol, Domiziano Mostacci and Vincenzo Molinari

Entropy 2018, 20(4), 233; https://doi.org/10.3390/e20040233 - 28 Mar 2018

Cited by 3 | Viewed by 3697

Abstract

The slowing down equation for elastic scattering of neutrons in an infinite homogeneous medium is solved analytically by decomposing the neutron energy spectrum into collision intervals. Since scattering physically smooths energy distributions by redistributing neutron energy uniformly, it is informative to observe how [...] Read more.

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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13 pages, 253 KiB

Open AccessArticle

Conformal Flattening for Deformed Information Geometries on the Probability Simplex ^†

by Atsumi Ohara

Entropy 2018, 20(3), 186; https://doi.org/10.3390/e20030186 - 10 Mar 2018

Cited by 5 | Viewed by 3232

Abstract

Recent progress of theories and applications regarding statistical models with generalized exponential functions in statistical science is giving an impact on the movement to deform the standard structure of information geometry. For this purpose, various representing functions are playing central roles. In this paper, we consider two important notions in information geometry, i.e., invariance and dual flatness, from a viewpoint of representing functions. We first characterize a pair of representing functions that realizes the invariant geometry by solving a system of ordinary differential equations. Next, by proposing a new transformation technique, i.e., conformal flattening, we construct dually flat geometries from a certain class of non-flat geometries. Finally, we apply the results to demonstrate several properties of gradient flows on the probability simplex. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

14 pages, 2922 KiB

Open AccessFeature PaperArticle

Equilibrium States in Two-Temperature Systems

by Evaldo M. F. Curado and Fernando D. Nobre

Entropy 2018, 20(3), 183; https://doi.org/10.3390/e20030183 - 9 Mar 2018

Cited by 8 | Viewed by 3466

Abstract

Systems characterized by more than one temperature usually appear in nonequilibrium statistical mechanics. In some cases, e.g., glasses, there is a temperature at which fast variables become thermalized, and another case associated with modes that evolve towards an equilibrium state in a very slow way. Recently, it was shown that a system of vortices interacting repulsively, considered as an appropriate model for type-II superconductors, presents an equilibrium state characterized by two temperatures. The main novelty concerns the fact that apart from the usual temperature T, related to fluctuations in particle velocities, an additional temperature

θ

was introduced, associated with fluctuations in particle positions. Since they present physically distinct characteristics, the system may reach an equilibrium state, characterized by finite and different values of these temperatures. In the application of type-II superconductors, it was shown that

θ ≫ T

, so that thermal effects could be neglected, leading to a consistent thermodynamic framework based solely on the temperature

θ

. In the present work, a more general situation, concerning a system characterized by two distinct temperatures

θ_{1}

and

θ_{2}

, which may be of the same order of magnitude, is discussed. These temperatures appear as coefficients of different diffusion contributions of a nonlinear Fokker-Planck equation. An H-theorem is proven, relating such a Fokker-Planck equation to a sum of two entropic forms, each of them associated with a given diffusion term; as a consequence, the corresponding stationary state may be considered as an equilibrium state, characterized by two temperatures. One of the conditions for such a state to occur is that the different temperature parameters,

θ_{1}

and

θ_{2}

, should be thermodynamically conjugated to distinct entropic forms,

S_{1}

and

S_{2}

, respectively. A functional

Λ [P] \equiv Λ (S_{1} [P], S_{2} [P])

is introduced, which presents properties characteristic of an entropic form; moreover, a thermodynamically conjugated temperature parameter

γ (θ_{1}, θ_{2})

can be consistently defined, so that an alternative physical description is proposed in terms of these pairs of variables. The physical consequences, and particularly, the fact that the equilibrium-state distribution, obtained from the Fokker-Planck equation, should coincide with the one from entropy extremization, are discussed. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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23 pages, 417 KiB

Open AccessFeature PaperArticle

Anomalous Statistics of Bose-Einstein Condensate in an Interacting Gas: An Effect of the Trap’s Form and Boundary Conditions in the Thermodynamic Limit

by Sergey Tarasov, Vladimir Kocharovsky and Vitaly Kocharovsky

Entropy 2018, 20(3), 153; https://doi.org/10.3390/e20030153 - 27 Feb 2018

Cited by 9 | Viewed by 4292

Abstract

We analytically calculate the statistics of Bose-Einstein condensate (BEC) fluctuations in an interacting gas trapped in a three-dimensional cubic or rectangular box with the Dirichlet, fused or periodic boundary conditions within the mean-field Bogoliubov and Thomas-Fermi approximations. We study a mesoscopic system of a finite number of trapped particles and its thermodynamic limit. We find that the BEC fluctuations, first, are anomalously large and non-Gaussian and, second, depend on the trap’s form and boundary conditions. Remarkably, these effects persist with increasing interparticle interaction and even in the thermodynamic limit—only the mean BEC occupation, not BEC fluctuations, becomes independent on the trap’s form and boundary conditions. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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9 pages, 245 KiB

Open AccessFeature PaperArticle

The Volume of Two-Qubit States by Information Geometry

by Milajiguli Rexiti, Domenico Felice and Stefano Mancini

Entropy 2018, 20(2), 146; https://doi.org/10.3390/e20020146 - 24 Feb 2018

Cited by 7 | Viewed by 3781

Abstract

Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled states with fixed purity. We show that the usage of the classical Fisher metric on phase space probability representation of quantum states gives the same qualitative results with respect to different versions of the quantum Fisher metric. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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11 pages, 270 KiB

Open AccessFeature PaperArticle

Energy from Negentropy of Non-Cahotic Systems

by Piero Quarati, Antonio M. Scarfone and Giorgio Kaniadakis

Entropy 2018, 20(2), 113; https://doi.org/10.3390/e20020113 - 9 Feb 2018

Cited by 3 | Viewed by 4551

Abstract

Negative contribution of entropy (negentropy) of a non-cahotic system, representing the potential of work, is a source of energy that can be transferred to an internal or inserted subsystem. In this case, the system loses order and its entropy increases. The subsystem increases its energy and can perform processes that otherwise would not happen, like, for instance, the nuclear fusion of inserted deuterons in liquid metal matrix, among many others. The role of positive and negative contributions of free energy and entropy are explored with their constraints. The energy available to an inserted subsystem during a transition from a non-equilibrium to the equilibrium chaotic state, when particle interaction (element of the system) is switched off, is evaluated. A few examples are given concerning some non-ideal systems and a possible application to the nuclear reaction screening problem is mentioned. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

12 pages, 625 KiB

Open AccessFeature PaperArticle

Strong- and Weak-Universal Critical Behaviour of a Mixed-Spin Ising Model with Triplet Interactions on the Union Jack (Centered Square) Lattice

by Jozef Strečka

Entropy 2018, 20(2), 91; https://doi.org/10.3390/e20020091 - 29 Jan 2018

Cited by 3 | Viewed by 4075

Abstract

The mixed spin-1/2 and spin-S Ising model on the Union Jack (centered square) lattice with four different three-spin (triplet) interactions and the uniaxial single-ion anisotropy is exactly solved by establishing a rigorous mapping equivalence with the corresponding zero-field (symmetric) eight-vertex model on a dual square lattice. A rigorous proof of the aforementioned exact mapping equivalence is provided by two independent approaches exploiting either a graph-theoretical or spin representation of the zero-field eight-vertex model. An influence of the interaction anisotropy as well as the uniaxial single-ion anisotropy on phase transitions and critical phenomena is examined in particular. It is shown that the considered model exhibits a strong-universal critical behaviour with constant critical exponents when considering the isotropic model with four equal triplet interactions or the anisotropic model with one triplet interaction differing from the other three. The anisotropic models with two different triplet interactions, which are pairwise equal to each other, contrarily exhibit a weak-universal critical behaviour with critical exponents continuously varying with a relative strength of the triplet interactions as well as the uniaxial single-ion anisotropy. It is evidenced that the variations of critical exponents of the mixed-spin Ising models with the integer-valued spins S differ basically from their counterparts with the half-odd-integer spins S. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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28 pages, 1430 KiB

Open AccessEditor’s ChoiceArticle

Minimising the Kullback–Leibler Divergence for Model Selection in Distributed Nonlinear Systems

by Oliver M. Cliff, Mikhail Prokopenko and Robert Fitch

Entropy 2018, 20(2), 51; https://doi.org/10.3390/e20020051 - 23 Jan 2018

Cited by 23 | Viewed by 8810

Abstract

The Kullback–Leibler (KL) divergence is a fundamental measure of information geometry that is used in a variety of contexts in artificial intelligence. We show that, when system dynamics are given by distributed nonlinear systems, this measure can be decomposed as a function of two information-theoretic measures, transfer entropy and stochastic interaction. More specifically, these measures are applicable when selecting a candidate model for a distributed system, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed acyclic graph (DAG) that characterises the unidirectional coupling between subsystems. Standard approaches to structure learning are not applicable in this framework due to the hidden variables; however, we can exploit the properties of certain dynamical systems to formulate exact methods based on differential topology. We approach the problem by using reconstruction theorems to derive an analytical expression for the KL divergence of a candidate DAG from the observed dataset. Using this result, we present a scoring function based on transfer entropy to be used as a subroutine in a structure learning algorithm. We then demonstrate its use in recovering the structure of coupled Lorenz and Rössler systems. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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415 KiB

Open AccessArticle

Oscillations in Multiparticle Production Processes

by Grzegorz Wilk and Zbigniew Włodarczyk

Entropy 2017, 19(12), 670; https://doi.org/10.3390/e19120670 - 6 Dec 2017

Cited by 5 | Viewed by 3755

Abstract

We discuss two examples of oscillations apparently hidden in some experimental results for high-energy multiparticle production processes: (i) the log-periodic oscillatory pattern decorating the power-like Tsallis distributions of transverse momenta; (ii) the oscillations of the modified combinants obtained from the measured multiplicity distributions. [...] Read more.

p p

data from the Large Hadron Collider (LHC). We show that in both cases, these phenomena can provide new insight into the dynamics of these processes. Full article

(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)

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