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

Deadline for manuscript submissions: closed (28 February 2021) | Viewed by 18604

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Prof. Dr. Dimitri Volchenkov

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Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA
Interests: data analysis; stochastic nonlinear dynamics; urban studies; complexity and uncertainty in the real-world systems
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Special Issue Information

Dear Colleagues,

Entropic forces are the emergent phenomena resulting from the entire system’s statistical tendency to increase its entropy. Entropic forces have attracted considerable attention as ways to reformulate, retrodict, and perhaps even “explain” classical Newtonian gravity from a rather specific thermodynamic perspective, as Verlinde suggested. Alex Wissner-Gross and Cameron Freer recently proposed “a causal generalization of entropic forces” that they showed can induce certain patterns of behavior with some very striking characteristics. One would not guess those outcomes by looking purely at the constraint that produces them. Underlying this set of intriguing behaviors is simply the computational capability to integrate over all possible futures to maximize the rate of entropy production over an entire trajectory. The observed behavior bears striking resemblance to examples we have seen in swarm intelligence (e.g., ant colonies, bird flocking, animal herding, bacterial growth, and fish schooling), communities, and in urban studies. The process of sampling alternative paths and behaviors reveals the essential features of quantum mechanics, one of which is the inclination of electrons to “explore all paths” that can be viewed as part of a search process, bounded in space by maximal causal entropy and in time by minimum coordination latency. In the proposed Special, we aim to organize a broad discussion on applications of the entropic force concept in studies of the real-world complex systems.

Prof. Dimitri Volchenkov
Guest Editor

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Keywords

entropic force
data clustering
colloids and depletion force
entropic gravity
entropic elasticity
swarm intelligence
entropic force in society and urban studies

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Published Papers (6 papers)

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Research

24 pages, 3239 KiB

Open AccessArticle

Scaling Analysis of an Image Encryption Scheme Based on Chaotic Dynamical Systems

by L. E. Reyes-López, J. S. Murguía, H. González-Aguilar, M. T. Ramírez-Torres, M. Mejía-Carlos and J. O. Armijo-Correa

Entropy 2021, 23(6), 672; https://doi.org/10.3390/e23060672 - 27 May 2021

Cited by 5 | Viewed by 2301

Abstract

Despite that many image encryption systems based on chaotic or hyperchaotic systems have been proposed to protect different kinds of information, it has been crucial to achieve as much security as possible in such systems. In this sense, we numerically implement a known image encryption system with some variants, making special emphasis when two operations are considered in the scrambling stage. The variants of such an encryption system are based on some hyperchaotic systems, which generated some substitution boxes and the keys of the system. With the aim to have a more complete evaluation, some internal stages of the image encryption scheme have been evaluated by using common statistical tests, and also the scaling behavior of the encrypted images has been calculated by means of a two-dimensional detrended fluctuation analysis (2D-DFA). Our results show that the image encryption systems that include two operations or transformations in the scrambling stage present a better performance than those encryption systems that consider just one operation. In fact, the 2D-DFA approach was more sensitive than some common statistical tests to determine more clearly the impact of multiple operations in the scrambling process, confirming that this scaling method can be used as a perceptual security metric, and it may contribute to having better image encryption systems. Full article

(This article belongs to the Special Issue Entropic Forces in Complex Systems)

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17 pages, 1954 KiB

Open AccessArticle

Infinite Ergodic Walks in Finite Connected Undirected Graphs

by Dimitri Volchenkov

Entropy 2021, 23(2), 205; https://doi.org/10.3390/e23020205 - 8 Feb 2021

Cited by 6 | Viewed by 2296

Abstract

The micro-canonical, canonical, and grand canonical ensembles of walks defined in finite connected undirected graphs are considered in the thermodynamic limit of infinite walk length. As infinitely long paths are extremely sensitive to structural irregularities and defects, their properties are used to describe the degree of structural imbalance, anisotropy, and navigability in finite graphs. For the first time, we introduce entropic force and pressure describing the effect of graph defects on mobility patterns associated with the very long walks in finite graphs; navigation in graphs and navigability to the nodes by the different types of ergodic walks; as well as node’s fugacity in the course of prospective network expansion or shrinking. Full article

(This article belongs to the Special Issue Entropic Forces in Complex Systems)

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15 pages, 1115 KiB

Open AccessArticle

Effects of Urban Producer Service Industry Agglomeration on Export Technological Complexity of Manufacturing in China

by Xinyu Gao, Chengpeng Lu and Jinhuang Mao

Entropy 2020, 22(10), 1108; https://doi.org/10.3390/e22101108 - 30 Sep 2020

Cited by 9 | Viewed by 3046

Abstract

Based on the measurement of producer service industry agglomeration and export technological complexity of manufactured products in 288 Chinese cities from 2000 to 2015, this paper illustrates the evolvement and spatial characteristics of the two factors through visualization figures, and discusses the effects of producer services agglomeration on export technological complexity of manufacturing through robust panel data models. The findings are as follows: as with the influence of industrial connection, empirical outcomes indicate that urban producer service agglomeration can promote technological complexity of export manufacturing on the full-sample level. Visualization analysis shows that the scale of producer service industry agglomeration and the export technological complexity of manufactured products around Chinese cities kept rising constantly during the study period. However, although the export technological complexity displayed a trickle-down effect, the producer service industry agglomeration experienced continuous polarization both on the national and the regional levels. Accordingly, as is shown in the empirical analysis by areas, regions with strong support from producer service industry saw a remarkable promotion in the export manufacturing technology, while the northwest and the northeast gradually lagged behind. Such results sufficiently prove that heterogeneity does exist in the performances of industrial connection between producer service industry and export manufacturing in cities of different regions in China. Full article

(This article belongs to the Special Issue Entropic Forces in Complex Systems)

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13 pages, 416 KiB

Open AccessArticle

Useful Dual Functional of Entropic Information Measures

by Angelo Plastino, Mario Carlos Rocca and Flavia Pennini

Entropy 2020, 22(4), 491; https://doi.org/10.3390/e22040491 - 24 Apr 2020

Cited by 1 | Viewed by 2680

Abstract

There are entropic functionals galore, but not simple objective measures to distinguish between them. We remedy this situation here by appeal to Born’s proposal, of almost a hundred years ago, that the square modulus of any wave function

{| ψ |}^{2}

be [...] Read more.

{| ψ |}^{2}

be regarded as a probability distribution P. the usefulness of using information measures like Shannon’s in this pure-state context has been highlighted in [Phys. Lett. A1993, 181, 446]. Here we will apply the notion with the purpose of generating a dual functional [

F_{α_{R}} : {S_{Q}} ⟶ R^{+}

], which maps entropic functionals onto positive real numbers. In such an endeavor, we use as standard ingredients the coherent states of the harmonic oscillator (CHO), which are unique in the sense of possessing minimum uncertainty. This use is greatly facilitated by the fact that the CHO can be given analytic, compact closed form as shown in [Rev. Mex. Fis. E 2019, 65, 191]. Rewarding insights are to be obtained regarding the comparison between several standard entropic measures. Full article

(This article belongs to the Special Issue Entropic Forces in Complex Systems)

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11 pages, 2175 KiB

Open AccessArticle

Research on the Node Importance of a Weighted Network Based on the K-Order Propagation Number Algorithm

by Pingchuan Tang, Chuancheng Song, Weiwei Ding, Junkai Ma, Jun Dong and Liya Huang

Entropy 2020, 22(3), 364; https://doi.org/10.3390/e22030364 - 22 Mar 2020

Cited by 15 | Viewed by 3980

Abstract

To describe both the global and local characteristics of a network more comprehensively, we propose the weighted K-order propagation number (WKPN) algorithm to extract the disease propagation based on the network topology to evaluate the node importance. Each node is set as the source of infection, and the total number of infected nodes is defined as the K-order propagation number after experiencing the propagation time K. The simulation of the symmetric network with bridge nodes indicated that the WKPN algorithm was more effective for evaluation of the algorithm features. A deliberate attack strategy, which indicated an attack on the network according to the node importance from high to low, was employed to evaluate the WKPN algorithm in real networks. Compared with the other methods tested, the results demonstrate the applicability and advancement that a lower number of nodes, with a higher importance calculated by the K-order propagation number algorithm, has to achieve full damage to the network structure. Full article

(This article belongs to the Special Issue Entropic Forces in Complex Systems)

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11 pages, 784 KiB

Open AccessArticle

Entropic Forces and Newton’s Gravitation

by Angelo Plastino and Mario Carlos Rocca

Entropy 2020, 22(3), 273; https://doi.org/10.3390/e22030273 - 27 Feb 2020

Cited by 4 | Viewed by 3125

Abstract

Our subject of interest here is entropic forces, as re-interpreted by Verlinde with reference to gravitation, that is, by appealing to Verlinde’s conception of an entropic (statistically emergent) gravity advanced in [Physica A 2018, 511, 139]. In a canonical ensemble framework, we will deal with a non relativistic quantum scenario. In it, we perform a non-relativistic Schrödinger treatment (ST) of gravity as an entropic force and are able to detect new kinds of bounded quantum gravitational states, not previously reported. These new bound states would provide us with a novel energy-source, not taken into account as yet. The present entropic force deviates from the Newton’s form only at extremely short distances. We propose, by specializing our results to gravitationally interacting bosons, a model for dark matter generation. Full article

(This article belongs to the Special Issue Entropic Forces in Complex Systems)

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