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Statistical Mechanics of Complex and Disordered Systems

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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 (31 July 2017) | Viewed by 69268

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Prof. Dr. Marcel Ausloos

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Guest Editor

1. School of Business,University of Leicester, Brookfield, Leicester LE2 1RQ, UK
2. Department of Statistics and Econometrics, Bucharest University of Economic Studies, 010374 Bucharest, Romania
Interests: econophysics; sociophysics; nonlinear dynamics; nonequilibrium systems; networks; phase transitions; growth (and decay) models; fractals; scientometrics; statistical physics; materials sciences and applied mathematics
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Janusz Miskiewicz

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Guest Editor

1. Institute of Theoretical Physics, University of Wrocław, Wrocław, Poland
2. Physics and Biophysics Department, Wrocław University of Enviromental and Life Sciences, Wrocław, Poland
Interests: econophysics; sociophysics; nonlinear dynamics; nonequilibrium systems; networks; phase transitions; growth (and decay) models; fractals; scientometrics; statistical physics; materials sciences; and applied mathematics

Special Issue Information

Dear Colleagues,

The field of Statistical Mechanics has found new investigation regimes due to the wide acceptance of phenomena within the realm of Complex and Disordered Systems. Beyond geometrical percolation studies, there appeared material studies such as on amorphous materials, and low dimensional aspects, for nanotechnologies. However, starting from the pioneering work of Montroll, much has been geared toward extensions in the socio-economic realm, close to society’s interest and so called soft science. The aim of this Special Issue is to encourage researchers to present original and recent developments on complex (quasi necessarily disordered) systems, grounded on theory and algorithms, in connection with the entropy concept, bearing in mind not only experimental or empirical features are of interest. It is expected that a coherent literature review is included in each manuscript not only to support definitive findings, but also to reveal controversies, pointing to the need for specific investigations in forthcoming work. The use of innovative methods, illustrated through modern examples, is expected to catch increasing attention from the research community on the concept of entropy. It goes without saying, that recent extensions of Shannon entropy is present in current research, quite apart from the classical aims found in equilibrium statistical mechanics. Networks should also be remembered as the underlying frames of investigations. In conclusion, much is expected from authors in order to establish connections between “entropy” and nonequilibrium (disordered) systems.

We look forward to reading your submissions.

Prof. Dr. Marcel Ausloos
Prof. Dr. Janusz Miskiewicz
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

disordered systems,
nonequilibrium systems,
percolation,
sociophysics,
modeling,
networks,
fractals

Published Papers (14 papers)

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Research

24 pages, 877 KiB

Open AccessArticle

Investigating the Configurations in Cross-Shareholding: A Joint Copula-Entropy Approach

by Roy Cerqueti, Giulia Rotundo and Marcel Ausloos

Entropy 2018, 20(2), 134; https://doi.org/10.3390/e20020134 - 20 Feb 2018

Cited by 16 | Viewed by 3751

Abstract

The complex nature of the interlacement of economic actors is quite evident at the level of the Stock market, where any company may actually interact with the other companies buying and selling their shares. In this respect, the companies populating a Stock market, along with their connections, can be effectively modeled through a directed network, where the nodes represent the companies, and the links indicate the ownership. This paper deals with this theme and discusses the concentration of a market. A cross-shareholding matrix is considered, along with two key factors: the node out-degree distribution which represents the diversification of investments in terms of the number of involved companies, and the node in-degree distribution which reports the integration of a company due to the sales of its own shares to other companies. While diversification is widely explored in the literature, integration is most present in literature on contagions. This paper captures such quantities of interest in the two frameworks and studies the stochastic dependence of diversification and integration through a copula approach. We adopt entropies as measures for assessing the concentration in the market. The main question is to assess the dependence structure leading to a better description of the data or to market polarization (minimal entropy) or market fairness (maximal entropy). In so doing, we derive information on the way in which the in- and out-degrees should be connected in order to shape the market. The question is of interest to regulators bodies, as witnessed by specific alert threshold published on the US mergers guidelines for limiting the possibility of acquisitions and the prevalence of a single company on the market. Indeed, all countries and the EU have also rules or guidelines in order to limit concentrations, in a country or across borders, respectively. The calibration of copulas and model parameters on the basis of real data serves as an illustrative application of the theoretical proposal. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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3998 KiB

Open AccessArticle

Comparative Statistical Mechanics of Muscle and Non-Muscle Contractile Systems: Stationary States of Near-Equilibrium Systems in A Linear Regime

by Yves Lecarpentier, Victor Claes, Xénophon Krokidis, Jean-Louis Hébert, Oumar Timbely, François-Xavier Blanc, Francine Michel and Alexandre Vallée

Entropy 2017, 19(10), 558; https://doi.org/10.3390/e19100558 - 20 Oct 2017

Cited by 8 | Viewed by 4202

Abstract

A. Huxley’s equations were used to determine the mechanical properties of muscle myosin II (MII) at the molecular level, as well as the probability of the occurrence of the different stages in the actin–myosin cycle. It was then possible to use the formalism of statistical mechanics with the grand canonical ensemble to calculate numerous thermodynamic parameters such as entropy, internal energy, affinity, thermodynamic flow, thermodynamic force, and entropy production rate. This allows us to compare the thermodynamic parameters of a non-muscle contractile system, such as the normal human placenta, with those of different striated skeletal muscles (soleus and extensor digitalis longus) as well as the heart muscle and smooth muscles (trachea and uterus) in the rat. In the human placental tissues, it was observed that the kinetics of the actin–myosin crossbridges were considerably slow compared with those of smooth and striated muscular systems. The entropy production rate was also particularly low in the human placental tissues, as compared with that observed in smooth and striated muscular systems. This is partly due to the low thermodynamic flow found in the human placental tissues. However, the unitary force of non-muscle myosin (NMII) generated by each crossbridge cycle in the myofibroblasts of the human placental tissues was similar in magnitude to that of MII in the myocytes of both smooth and striated muscle cells. Statistical mechanics represents a powerful tool for studying the thermodynamics of all contractile muscle and non-muscle systems. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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345 KiB

Open AccessArticle

Backtracking and Mixing Rate of Diffusion on Uncorrelated Temporal Networks

by Martin Gueuning, Renaud Lambiotte and Jean-Charles Delvenne

Entropy 2017, 19(10), 542; https://doi.org/10.3390/e19100542 - 13 Oct 2017

Cited by 5 | Viewed by 3743

Abstract

We consider the problem of diffusion on temporal networks, where the dynamics of each edge is modelled by an independent renewal process. Despite the apparent simplicity of the model, the trajectories of a random walker exhibit non-trivial properties. Here, we quantify the walker’s tendency to backtrack at each step (return where he/she comes from), as well as the resulting effect on the mixing rate of the process. As we show through empirical data, non-Poisson dynamics may significantly slow down diffusion due to backtracking, by a mechanism intrinsically different from the standard bus paradox and related temporal mechanisms. We conclude by discussing the implications of our work for the interpretation of results generated by null models of temporal networks. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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1780 KiB

Open AccessArticle

Decomposition of the Inequality of Income Distribution by Income Types—Application for Romania

by Tudorel Andrei, Bogdan Oancea, Peter Richmond, Gurjeet Dhesi and Claudiu Herteliu

Entropy 2017, 19(9), 430; https://doi.org/10.3390/e19090430 - 01 Sep 2017

Cited by 7 | Viewed by 5402

Abstract

This paper identifies the salient factors that characterize the inequality income distribution for Romania. Data analysis is rigorously carried out using sophisticated techniques borrowed from classical statistics (Theil). Decomposition of the inequalities measured by the Theil index is also performed. This study relies [...] Read more.

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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703 KiB

Open AccessArticle

The KCOD Model on (3,4,6,4) and (3⁴,6) Archimedean Lattices

by Francisco W. De Sousa Lima

Entropy 2017, 19(9), 459; https://doi.org/10.3390/e19090459 - 31 Aug 2017

Cited by 2 | Viewed by 3759

Abstract

Through Monte Carlo simulations, we studied the critical properties of kinetic models of continuous opinion dynamics on (

3, 4, 6, 4

) and (

3^{4}, 6

) Archimedean lattices. We obtain

p_{c}

and the critical exponents’ [...] Read more.

Through Monte Carlo simulations, we studied the critical properties of kinetic models of continuous opinion dynamics on (

3, 4, 6, 4

) and (

3^{4}, 6

) Archimedean lattices. We obtain

p_{c}

and the critical exponents’ ratio from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical points and Binder cumulant are

p_{c} = 0.085 (6)

and

O_{4}^{*} = 0.605 (9)

; and

p_{c} = 0.146 (5)

and

O_{4}^{*} = 0.606 (3)

for (

3, 4, 6, 4

) and (

3^{4}, 6

) lattices, respectively, while the exponent ratios

β / ν

γ / ν

and

1 / ν

are, respectively:

0.126 (1)

1.50 (7)

, and

0.90 (5)

for (

3, 4, 6, 4

); and

0.125 (3)

1.54 (6)

, and

0.99 (3)

for (

3^{4}, 6

) lattices. Our new results agree with majority-vote model on previously studied regular lattices and disagree with the Ising model on square-lattice. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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264 KiB

Open AccessArticle

Assessing the Role of Strategic Choice on Organizational Performance by Jacquemin–Berry Entropy Index

by Sebastian Ion Ceptureanu, Eduard Gabriel Ceptureanu and Irinel Marin

Entropy 2017, 19(9), 448; https://doi.org/10.3390/e19090448 - 27 Aug 2017

Cited by 19 | Viewed by 4818

Abstract

This paper investigates effects of strategic choice on organizational performance for Romanian family-owned Small and Medium sized Enterprises (SMEs). Using adapted Jacquemin–Berry entropy index for both product and international diversification and using a regression model, our study discusses family involvement as a moderating factor for organizational performance assessment. We discovered that there are multiple interactions between strategic choice and organizational performance while family involvement fails to have a significant role in moderating these interactions. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

1058 KiB

Open AccessArticle

Power-Law Distributions from Sigma-Pi Structure of Sums of Random Multiplicative Processes

by Arthur Matsuo Yamashita Rios de Sousa, Hideki Takayasu, Didier Sornette and Misako Takayasu

Entropy 2017, 19(8), 417; https://doi.org/10.3390/e19080417 - 17 Aug 2017

Cited by 3 | Viewed by 6490

Abstract

We introduce a simple growth model in which the sizes of entities evolve as multiplicative random processes that start at different times. A novel aspect we examine is the dependence among entities. For this, we consider three classes of dependence between growth factors governing the evolution of sizes: independence, Kesten dependence and mixed dependence. We take the sum X of the sizes of the entities as the representative quantity of the system, which has the structure of a sum of product terms (Sigma-Pi), whose asymptotic distribution function has a power-law tail behavior. We present evidence that the dependence type does not alter the asymptotic power-law tail behavior, nor the value of the tail exponent. However, the structure of the large values of the sum X is found to vary with the dependence between the growth factors (and thus the entities). In particular, for the independence case, we find that the large values of X are contributed by a single maximum size entity: the asymptotic power-law tail is the result of such single contribution to the sum, with this maximum contributing entity changing stochastically with time and with realizations. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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447 KiB

Open AccessArticle

Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders

by Arkadiusz Jędrzejewski and Katarzyna Sznajd-Weron

Entropy 2017, 19(8), 415; https://doi.org/10.3390/e19080415 - 13 Aug 2017

Cited by 20 | Viewed by 5825

Abstract

We study the q-voter model driven by stochastic noise arising from one out of two types of nonconformity: anticonformity or independence. We compare two approaches that were inspired by the famous psychological controversy known as the person–situation debate. We relate the person approach with the quenched disorder and the situation approach with the annealed disorder, and investigate how these two approaches influence order–disorder phase transitions observed in the q-voter model with noise. We show that under a quenched disorder, differences between models with independence and anticonformity are weaker and only quantitative. In contrast, annealing has a much more profound impact on the system and leads to qualitative differences between models on a macroscopic level. Furthermore, only under an annealed disorder may the discontinuous phase transitions appear. It seems that freezing the agents’ behavior at the beginning of simulation—introducing quenched disorder—supports second-order phase transitions, whereas allowing agents to reverse their attitude in time—incorporating annealed disorder—supports discontinuous ones. We show that anticonformity is insensitive to the type of disorder, and in all cases it gives the same result. We precede our study with a short insight from statistical physics into annealed vs. quenched disorder and a brief review of these two approaches in models of opinion dynamics. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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1194 KiB

Open AccessArticle

Relationship between Entropy, Corporate Entrepreneurship and Organizational Capabilities in Romanian Medium Sized Enterprises

by Eduard Gabriel Ceptureanu, Sebastian Ion Ceptureanu and Doina I. Popescu

Entropy 2017, 19(8), 412; https://doi.org/10.3390/e19080412 - 10 Aug 2017

Cited by 24 | Viewed by 6185

Abstract

This paper analyses the relations between entropy, organizational capabilities and corporate entrepreneurship. The results indicate strong links between strategy and corporate entrepreneurship, moderated by the organizational capabilities. We find that companies with strong organizational capabilities, using a systematic strategic approach, widely use corporate entrepreneurship as an instrument to fulfil their objectives. Our study contributes to the limited amount of empirical research on entropy in an organization setting by highlighting the boundary conditions of the impact by examining the moderating effect of firms’ organizational capabilities and also to the development of Econophysics as a fast growing area of interdisciplinary sciences. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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617 KiB

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Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior

by Vygintas Gontis and Aleksejus Kononovicius

Entropy 2017, 19(8), 387; https://doi.org/10.3390/e19080387 - 27 Jul 2017

Cited by 10 | Viewed by 3950

Abstract

The origin of the long-range memory in non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases, the notion of spurious memory is introduced. A good example of Markov processes with spurious memory is a stochastic process driven by a non-linear stochastic differential equation (SDE). This example is at odds with models built using fractional Brownian motion (fBm). We analyze the differences between these two cases seeking to establish possible empirical tests of the origin of the observed long-range memory. We investigate probability density functions (PDFs) of burst and inter-burst duration in numerically-obtained time series and compare with the results of fBm. Our analysis confirms that the characteristic feature of the processes described by a one-dimensional SDE is the power-law exponent

3 / 2

of the burst or inter-burst duration PDF. This property of stochastic processes might be used to detect spurious memory in various non-equilibrium systems, where observed macroscopic behavior can be derived from the imitative interactions of agents. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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850 KiB

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Conformity, Anticonformity and Polarization of Opinions: Insights from a Mathematical Model of Opinion Dynamics

by Tyll Krueger, Janusz Szwabiński and Tomasz Weron

Entropy 2017, 19(7), 371; https://doi.org/10.3390/e19070371 - 19 Jul 2017

Cited by 43 | Viewed by 7479

Abstract

Understanding and quantifying polarization in social systems is important because of many reasons. It could for instance help to avoid segregation and conflicts in the society or to control polarized debates and predict their outcomes. In this paper, we present a version of the q-voter model of opinion dynamics with two types of responses to social influence: conformity (like in the original q-voter model) and anticonformity. We put the model on a social network with the double-clique topology in order to check how the interplay between those responses impacts the opinion dynamics in a population divided into two antagonistic segments. The model is analyzed analytically, numerically and by means of Monte Carlo simulations. Our results show that the system undergoes two bifurcations as the number of cross-links between cliques changes. Below the first critical point, consensus in the entire system is possible. Thus, two antagonistic cliques may share the same opinion only if they are loosely connected. Above that point, the system ends up in a polarized state. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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479 KiB

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An Alternative for Indicators that Characterize the Structure of Economic Systems

by Irina-Maria Dragan and Alexandru Isaic-Maniu

Entropy 2017, 19(7), 346; https://doi.org/10.3390/e19070346 - 10 Jul 2017

Cited by 8 | Viewed by 3070

Abstract

Studies on the structure of economic systems are, most frequently, carried out by the methods of informational statistics. These methods, often accompanied by a broad range of indicators (Shannon entropy, Balassa coefficient, Herfindahl specialty index, Gini coefficient, Theil index, etc.) around which a wide literature has been created over time, have a major disadvantage. Their weakness is related to the imposition of the system condition, which indicates the need to know all of the components of the system (as absolute values or as weights). This restriction is difficult to accomplish in some situations, while in others this knowledge may be irrelevant, especially when there is an interest in structural changes only in some of the components of the economic system (either we refer to the typology of economic activities—NACE, or of territorial units—Nomenclature of territorial units for statistics (NUTS)). This article presents a procedure for characterizing the structure of a system and for comparing its evolution over time, in the case of incomplete information, thus eliminating the restriction existent in the classical methods. The proposed methodological alternative uses a parametric distribution, with sub-unit values for the variable. The application refers to Gross Domestic Product values for five of the 28 European Union countries, with annual values of over 1000 billion Euros (Germany, Spain, France, Italy, and United Kingdom) for the years 2003 and 2015. A form of the Wald sequential test is applied to measure changes in the structure of this group of countries, between the years compared. The results of this application validate the proposed method. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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559 KiB

Open AccessArticle

Glassy States of Aging Social Networks

by Foroogh Hassanibesheli, Leila Hedayatifar, Hadise Safdari, Marcel Ausloos and G. Reza Jafari

Entropy 2017, 19(6), 246; https://doi.org/10.3390/e19060246 - 30 May 2017

Cited by 21 | Viewed by 5200

Abstract

Individuals often develop reluctance to change their social relations, called “secondary homebody”, even though their interactions with their environment evolve with time. Some memory effect is loosely present deforcing changes. In other words, in the presence of memory, relations do not change easily. In order to investigate some history or memory effect on social networks, we introduce a temporal kernel function into the Heider conventional balance theory, allowing for the “quality” of past relations to contribute to the evolution of the system. This memory effect is shown to lead to the emergence of aged networks, thereby perfectly describing—and what is more, measuring—the aging process of links (“social relations”). It is shown that such a memory does not change the dynamical attractors of the system, but does prolong the time necessary to reach the “balanced states”. The general trend goes toward obtaining either global (“paradise” or “bipolar”) or local (“jammed”) balanced states, but is profoundly affected by aged relations. The resistance of elder links against changes decelerates the evolution of the system and traps it into so named glassy states. In contrast to balance configurations which live on stable states, such long-lived glassy states can survive in unstable states. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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675 KiB

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Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis

by Luis L. Bonilla, Manuel Carretero and Filippo Terragni

Entropy 2017, 19(5), 209; https://doi.org/10.3390/e19050209 - 04 May 2017

Cited by 6 | Viewed by 4279

Abstract

In this work, we present a numerical study of the influence of matrix degrading enzyme (MDE) dynamics and haptotaxis on the development of vessel networks in tumor-induced angiogenesis. Avascular tumors produce growth factors that induce nearby blood vessels to emit sprouts formed by endothelial cells. These capillary sprouts advance toward the tumor by chemotaxis (gradients of growth factor) and haptotaxis (adhesion to the tissue matrix outside blood vessels). The motion of the capillaries in this constrained space is modelled by stochastic processes (Langevin equations, branching and merging of sprouts) coupled to continuum equations for concentrations of involved substances. There is a complementary deterministic description in terms of the density of actively moving tips of vessel sprouts. The latter forms a stable soliton-like wave whose motion is influenced by the different taxis mechanisms. We show the delaying effect of haptotaxis on the advance of the angiogenic vessel network by direct numerical simulations of the stochastic process and by a study of the soliton motion. Full article

(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)

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