Editorial

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Open AccessEditorial

by Hermann Haken and Juval Portugali

Entropy 2017, 19(1), 18; https://doi.org/10.3390/e19010018 - 31 Dec 2016

Cited by 23 | Viewed by 7988

The process of “self-organization” takes place in open and complex systems that acquire spatio-temporal or functional structures without specific ordering instructions from the outside. [...] Full article

(This article belongs to the Special Issue Information and Self-Organization)

Research

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6775 KiB

Open AccessArticle

On Macrostates in Complex Multi-Scale Systems

by Harald Atmanspacher

Entropy 2016, 18(12), 426; https://doi.org/10.3390/e18120426 - 29 Nov 2016

Cited by 18 | Viewed by 6732

Abstract

A characteristic feature of complex systems is their deep structure, meaning that the definition of their states and observables depends on the level, or the scale, at which the system is considered. This scale dependence is reflected in the distinction of micro- and [...] Read more.

A characteristic feature of complex systems is their deep structure, meaning that the definition of their states and observables depends on the level, or the scale, at which the system is considered. This scale dependence is reflected in the distinction of micro- and macro-states, referring to lower and higher levels of description. There are several conceptual and formal frameworks to address the relation between them. Here, we focus on an approach in which macrostates are contextually emergent from (rather than fully reducible to) microstates and can be constructed by contextual partitions of the space of microstates. We discuss criteria for the stability of such partitions, in particular under the microstate dynamics, and outline some examples. Finally, we address the question of how macrostates arising from stable partitions can be identified as relevant or meaningful. Full article

(This article belongs to the Special Issue Information and Self-Organization)

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797 KiB

Open AccessArticle

Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality

by Lowell F. Thompson and Hong Qian

Entropy 2016, 18(8), 309; https://doi.org/10.3390/e18080309 - 18 Aug 2016

Cited by 6 | Viewed by 4847

Abstract

In this paper, we revisit the notion of the “minus logarithm of stationary probability” as a generalized potential in nonequilibrium systems and attempt to illustrate its central role in an axiomatic approach to stochastic nonequilibrium thermodynamics of complex systems. It is demonstrated that [...] Read more.

In this paper, we revisit the notion of the “minus logarithm of stationary probability” as a generalized potential in nonequilibrium systems and attempt to illustrate its central role in an axiomatic approach to stochastic nonequilibrium thermodynamics of complex systems. It is demonstrated that this quantity arises naturally through both monotonicity results of Markov processes and as the rate function when a stochastic process approaches a deterministic limit. We then undertake a more detailed mathematical analysis of the consequences of this quantity, culminating in a necessary and sufficient condition for the criticality of stochastic systems. This condition is then discussed in the context of recent results about criticality in biological systems. Full article

(This article belongs to the Special Issue Information and Self-Organization)

11424 KiB

Open AccessArticle

Information and Selforganization: A Unifying Approach and Applications

by Hermann Haken and Juval Portugali

Entropy 2016, 18(6), 197; https://doi.org/10.3390/e18060197 - 14 Jun 2016

Cited by 34 | Viewed by 8204

Abstract

Selforganization is a process by which the interaction between the parts of a complex system gives rise to the spontaneous emergence of patterns, structures or functions. In this interaction the system elements exchange matter, energy and information. We focus our attention on the [...] Read more.

Selforganization is a process by which the interaction between the parts of a complex system gives rise to the spontaneous emergence of patterns, structures or functions. In this interaction the system elements exchange matter, energy and information. We focus our attention on the relations between selforganization and information in general and the way they are linked to cognitive processes in particular. We do so from the analytical and mathematical perspective of the “second foundation of synergetics” and its “synergetic computer” and with reference to several forms of information: Shannon’s information that deals with the quantity of a message irrespective of its meaning, semantic and pragmatic forms of information that deal with the meaning conveyed by messages and information adaptation that refers to the interplay between Shannon’s information and semantic or pragmatic information. We first elucidate the relations between selforganization and information theoretically and mathematically and then by means of specific case studies. Full article

(This article belongs to the Special Issue Information and Self-Organization)

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239 KiB

Open AccessArticle

Entropy and the Self-Organization of Information and Value

by Rainer Feistel and Werner Ebeling

Entropy 2016, 18(5), 193; https://doi.org/10.3390/e18050193 - 19 May 2016

Cited by 23 | Viewed by 6895

Abstract

Adam Smith, Charles Darwin, Rudolf Clausius, and Léon Brillouin considered certain “values” as key quantities in their descriptions of market competition, natural selection, thermodynamic processes, and information exchange, respectively. None of those values can be computed from elementary properties of the particular object [...] Read more.

Adam Smith, Charles Darwin, Rudolf Clausius, and Léon Brillouin considered certain “values” as key quantities in their descriptions of market competition, natural selection, thermodynamic processes, and information exchange, respectively. None of those values can be computed from elementary properties of the particular object they are attributed to, but rather values represent emergent, irreducible properties. In this paper, such values are jointly understood as information values in certain contexts. For this aim, structural information is distinguished from symbolic information. While the first can be associated with arbitrary physical processes or structures, the latter requires conventions which govern encoding and decoding of the symbols which form a message. As a value of energy, Clausius’ entropy is a universal measure of the structural information contained in a thermodynamic system. The structural information of a message, in contrast to its meaning, can be evaluated by Shannon’s entropy of communication. Symbolic information is found only in the realm of life, such as in animal behavior, human sociology, science, or technology, and is often cooperatively valuated by competition. Ritualization is described here as a universal scenario for the self-organization of symbols by which symbolic information emerges from structural information in the course of evolution processes. Emergent symbolic information exhibits the novel fundamental code symmetry which prevents the meaning of a message from being reducible to the physical structure of its carrier. While symbols turn arbitrary during the ritualization transition, their structures preserve information about their evolution history. Full article

(This article belongs to the Special Issue Information and Self-Organization)

409 KiB

Open AccessArticle

Stochastic Resonance, Self-Organization and Information Dynamics in Multistable Systems

by Grégoire Nicolis and Catherine Nicolis

Entropy 2016, 18(5), 172; https://doi.org/10.3390/e18050172 - 04 May 2016

Cited by 14 | Viewed by 5547

Abstract

A class of complex self-organizing systems subjected to fluctuations of environmental or intrinsic origin and to nonequilibrium constraints in the form of an external periodic forcing is analyzed from the standpoint of information theory. Conditions under which the response of information entropy and [...] Read more.

A class of complex self-organizing systems subjected to fluctuations of environmental or intrinsic origin and to nonequilibrium constraints in the form of an external periodic forcing is analyzed from the standpoint of information theory. Conditions under which the response of information entropy and related quantities to the nonequilibrium constraint can be optimized via a stochastic resonance-type mechanism are identified, and the role of key parameters is assessed. Full article

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1372 KiB

Open AccessArticle

An Evolutionary Game Theoretic Approach to Multi-Sector Coordination and Self-Organization

by Fernando P. Santos, Sara Encarnação, Francisco C. Santos, Juval Portugali and Jorge M. Pacheco

Entropy 2016, 18(4), 152; https://doi.org/10.3390/e18040152 - 20 Apr 2016

Cited by 18 | Viewed by 9219

Abstract

Coordination games provide ubiquitous interaction paradigms to frame human behavioral features, such as information transmission, conventions and languages as well as socio-economic processes and institutions. By using a dynamical approach, such as Evolutionary Game Theory (EGT), one is able to follow, in detail, [...] Read more.

Coordination games provide ubiquitous interaction paradigms to frame human behavioral features, such as information transmission, conventions and languages as well as socio-economic processes and institutions. By using a dynamical approach, such as Evolutionary Game Theory (EGT), one is able to follow, in detail, the self-organization process by which a population of individuals coordinates into a given behavior. Real socio-economic scenarios, however, often involve the interaction between multiple co-evolving sectors, with specific options of their own, that call for generalized and more sophisticated mathematical frameworks. In this paper, we explore a general EGT approach to deal with coordination dynamics in which individuals from multiple sectors interact. Starting from a two-sector, consumer/producer scenario, we investigate the effects of including a third co-evolving sector that we call public. We explore the changes in the self-organization process of all sectors, given the feedback that this new sector imparts on the other two. Full article

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1271 KiB

Open AccessArticle

Self-Organization with Constraints—A Mathematical Model for Functional Differentiation

by Ichiro Tsuda, Yutaka Yamaguti and Hiroshi Watanabe

Entropy 2016, 18(3), 74; https://doi.org/10.3390/e18030074 - 26 Feb 2016

Cited by 7 | Viewed by 7303

Abstract

This study proposes mathematical models for functional differentiations that are viewed as self-organization with external constraints. From the viewpoint of system development, the present study investigates how system components emerge under the presence of constraints that act on a whole system. Cell differentiation [...] Read more.

This study proposes mathematical models for functional differentiations that are viewed as self-organization with external constraints. From the viewpoint of system development, the present study investigates how system components emerge under the presence of constraints that act on a whole system. Cell differentiation in embryos and functional differentiation in cortical modules are typical examples of this phenomenon. In this paper, as case studies, we deal with three mathematical models that yielded components via such global constraints: the genesis of neuronal elements, the genesis of functional modules, and the genesis of neuronal interactions. The overall development of a system may follow a certain variational principle. Full article

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701 KiB

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Measuring the Complexity of Continuous Distributions

by Guillermo Santamaría-Bonfil, Nelson Fernández and Carlos Gershenson

Entropy 2016, 18(3), 72; https://doi.org/10.3390/e18030072 - 26 Feb 2016

Cited by 9 | Viewed by 8984

Abstract

We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. Given that the measures were based on Shannon’s information, the novel continuous complexity measures describe how a system’s predictability changes in terms of the probability distribution parameters. [...] Read more.

We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. Given that the measures were based on Shannon’s information, the novel continuous complexity measures describe how a system’s predictability changes in terms of the probability distribution parameters. This allows us to calculate the complexity of phenomena for which distributions are known. We find that a broad range of common parameters found in Gaussian and scale-free distributions present high complexity values. We also explore the relationship between our measure of complexity and information adaptation. Full article

(This article belongs to the Special Issue Information and Self-Organization)

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Review

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Open AccessReview

Increase in Complexity and Information through Molecular Evolution

by Peter Schuster

Entropy 2016, 18(11), 397; https://doi.org/10.3390/e18110397 - 14 Nov 2016

Cited by 11 | Viewed by 5999

Abstract

Biological evolution progresses by essentially three different mechanisms: (I) optimization of properties through natural selection in a population of competitors; (II) development of new capabilities through cooperation of competitors caused by catalyzed reproduction; and (III) variation of genetic information through mutation or recombination. [...] Read more.

Biological evolution progresses by essentially three different mechanisms: (I) optimization of properties through natural selection in a population of competitors; (II) development of new capabilities through cooperation of competitors caused by catalyzed reproduction; and (III) variation of genetic information through mutation or recombination. Simplified evolutionary processes combine two out of the three mechanisms: Darwinian evolution combines competition (I) and variation (III) and is represented by the quasispecies model, major transitions involve cooperation (II) of competitors (I), and the third combination, cooperation (II) and variation (III) provides new insights in the role of mutations in evolution. A minimal kinetic model based on simple molecular mechanisms for reproduction, catalyzed reproduction and mutation is introduced, cast into ordinary differential equations (ODEs), and analyzed mathematically in form of its implementation in a flow reactor. Stochastic aspects are investigated through computer simulation of trajectories of the corresponding chemical master equations. The competition-cooperation model, mechanisms (I) and (II), gives rise to selection at low levels of resources and leads to symbiontic cooperation in case the material required is abundant. Accordingly, it provides a kind of minimal system that can undergo a (major) transition. Stochastic effects leading to extinction of the population through self-enhancing oscillations destabilize symbioses of four or more partners. Mutations (III) are not only the basis of change in phenotypic properties but can also prevent extinction provided the mutation rates are sufficiently large. Threshold phenomena are observed for all three combinations: The quasispecies model leads to an error threshold, the competition-cooperation model allows for an identification of a resource-triggered bifurcation with the transition, and for the cooperation-mutation model a kind of stochastic threshold for survival through sufficiently high mutation rates is observed. The evolutionary processes in the model are accompanied by gains in information on the environment of the evolving populations. In order to provide a useful basis for comparison, two forms of information, syntactic or Shannon information and semantic information are introduced here. Both forms of information are defined for simple evolving systems at the molecular level. Selection leads primarily to an increase in semantic information in the sense that higher fitness allows for more efficient exploitation of the environment and provides the basis for more progeny whereas understanding transitions involves characteristic contributions from both Shannon information and semantic information. Full article

(This article belongs to the Special Issue Information and Self-Organization)

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