Showing papers in "Entropy in 2010"
TL;DR: It is shown that a new wide class of Gamma-divergences can be generated not only from the family of Beta-diversgences but also from a family of Alpha-d divergences.
Abstract: In this paper, we extend and overview wide families of Alpha-, Beta- and Gamma-divergences and discuss their fundamental properties. In literature usually only one single asymmetric (Alpha, Beta or Gamma) divergence is considered. We show in this paper that there exist families of such divergences with the same consistent properties. Moreover, we establish links and correspondences among these divergences by applying suitable nonlinear transformations. For example, we can generate the Beta-divergences directly from Alpha-divergences and vice versa. Furthermore, we show that a new wide class of Gamma-divergences can be generated not only from the family of Beta-divergences but also from a family of Alpha-divergences. The paper bridges these divergences and shows also their links to Tsallis and Renyi entropies. Most of these divergences have a natural information theoretic interpretation.
485 citations
TL;DR: The goal of this paper is the extension of the Shannon entropy method for the imprecise data, especially interval and fuzzy data cases.
Abstract: Finding the appropriate weight for each criterion is one of the main points in Multi Attribute Decision Making (MADM) problems. Shannon’s entropy method is one of the various methods for finding weights discussed in the literature. However, in many real life problems, the data for the decision making processes cannot be measured precisely and there may be some other types of data, for instance, interval data and fuzzy data. The goal of this paper is the extension of the Shannon entropy method for the imprecise data, especially interval and fuzzy data cases.
273 citations
TL;DR: This review first offers a brief summary on the methodological and formal foundations of complex networks, then it attempts a general vision of research activity on language from a complex networks perspective, and specially highlights efforts with cognitive-inspired aim.
Abstract: During the last ten years several studies have appeared regarding language complexity. Research on this issue began soon after the burst of a new movement of interest and research in the study of complex networks, i.e., networks whose structure is irregular, complex and dynamically evolving in time. In the first years, network approach to language mostly focused on a very abstract and general overview of language complexity, and few of them studied how this complexity is actually embodied in humans or how it affects cognition. However research has slowly shifted from the language-oriented towards a more cognitive-oriented point of view. This review first offers a brief summary on the methodological and formal foundations of complex networks, then it attempts a general vision of research activity on language from a complex networks perspective, and specially highlights those efforts with cognitive-inspired aim.
188 citations
TL;DR: An extensive survey of the papers pertaining to the thermodynamic approach to tribosystems, particularly using the concept of entropy as a natural time base, is presented with a summary of the important contributions of leading researchers.
Abstract: An extensive survey of the papers pertaining to the thermodynamic approach to tribosystems, particularly using the concept of entropy as a natural time base, is presented with a summary of the important contributions of leading researchers.
158 citations
TL;DR: Some of the criticism against and evidence in favor of autocatalytic sets are reviewed, and a case for their plausibility is made based on a formal framework that was introduced and studied in the previous work.
Abstract: The origin of life is one of the most fundamental, but also one of the most difficult problems in science. Despite differences between various proposed scenarios, one common element seems to be the emergence of an autocatalytic set or cycle at some stage. However, there is still disagreement as to how likely it is that such self-sustaining sets could arise “spontaneously”. This disagreement is largely caused by the lack of formal models. Here, we briefly review some of the criticism against and evidence in favor of autocatalytic sets, and then make a case for their plausibility based on a formal framework that was introduced and studied in our previous work.
150 citations
TL;DR: The theoretical and experimental development of quantum simulation using quantum computers is surveyed, from the first ideas to the intense research efforts currently underway.
Abstract: Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beginning of the field in the 1980s Moreover, useful results beyond the reach of classical computation are expected to be accessible with fewer than a hundred qubits, making quantum simulation potentially one of the earliest practical applications of quantum computers In this paper we survey the theoretical and experimental development of quantum simulation using quantum computers, from the first ideas to the intense research efforts currently underway
142 citations
TL;DR: Advantages of entropy-based genetic diversity measures, at levels from gene expression to landscapes, are highlighted, to identify the formal connections between genetic diversity and the flow of information to and from the environment.
Abstract: This article highlights advantages of entropy-based genetic diversity measures, at levels from gene expression to landscapes. Shannon’s entropy-based diversity is the standard for ecological communities. The exponentials of Shannon’s and the related “mutual information” excel in their ability to express diversity intuitively, and provide a generalised method of considering microscopic behaviour to make macroscopic predictions, under given conditions. The hierarchical nature of entropy and information allows integrated modeling of diversity along one DNA sequence, and between different sequences within and among populations, species, etc. The aim is to identify the formal connections between genetic diversity and the flow of information to and from the environment.
86 citations
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TL;DR: The principle of least action provides a holistic worldview in which Nature in its entirety and every detail is described in terms of actions, which recognizes any fundamental difference between fundamental particles and fundamental forces.
Abstract: The principle of least action provides a holistic worldview in which Nature in its entirety and every detail is described in terms of actions. Each and every action is ultimately composed of one or multiple of the most elementary actions which relates to Planck’s constant. Elements of space are closed actions, known as fermions, whereas elements of time are open actions, known as bosons. The actions span an energy landscape, the Universe, which evolves irreversibly according to the 2nd law of thermodynamics by diminishing energy density differences in least time. During evolution densely-curled actions unfold step-by-step when opening up and expelling one or multiple elementary actions to their surrounding sparser space. The energy landscape will process from one symmetry group to another until the equivalence to its dual, i.e., the surrounding density has been attained. The scale-free physical portrayal of nature in terms of actions does not recognize any fundamental difference between fundamental particles and fundamental forces. Instead a plethora of particles and a diaspora of forces are perceived merely as diverse manifestations of a natural selection for various mechanisms and ways to decrease free energy in the least time.
81 citations
TL;DR: In this paper, the authors study the properties of functionals which are invariant with respect to monotonic transformations and derive Lyapunov functionals for Markov chains.
Abstract: The focus of this article is on entropy and Markov processes We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant “additivity” properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order) The solution differs significantly from the ordering given by the inequality of entropy growth For inference, this approach results in a convex compact set of conditionally “most random” distributions
81 citations
TL;DR: A short overview of black hole entropy in alternative gravitational theories is presented, which focuses on metric and Palatini ƒ(R) gravity and on scalar-tensor theories.
Abstract: A short overview of black hole entropy in alternative gravitational theories is presented. Motivated by the recent attempts to explain the cosmic acceleration without dark energy, we focus on metric and Palatini ƒ(R) gravity and on scalar-tensor theories.
77 citations
TL;DR: The objective of this paper is to answer the frequently asked question “is there any practical application of the thermodynamics in the study of friction and wear?” and to show that the thermodynamic methods have potential for both fundamental study ofriction and wear and for the development of new materials.
Abstract: The paper discusses the concept of entropy as applied to friction and wear. Friction and wear are classical examples of irreversible dissipative processes, and it is widely recognized that entropy generation is their important quantitative measure. On the other hand, the use of thermodynamic methods in tribology remains controversial and questions about the practical usefulness of these methods are often asked. A significant part of entropic tribological research was conducted in Russia since the 1970s. Surprisingly, many of these studies are not available in English and still not well known in the West. The paper reviews various views on the role of entropy and self-organization in tribology and it discusses modern approaches to wear and friction, which use the thermodynamic entropic method as well as the application of the mathematical concept of entropy to the dynamic friction effects (e.g., the running-in transient process, stick-slip motion, etc.) and a possible connection between the thermodynamic and information approach. The paper also discusses non-equilibrium thermodynamic approach to friction, wear, and self-healing. In general, the objective of this paper is to answer the frequently asked question “is there any practical application of the thermodynamics in the study of friction and wear?” and to show that the thermodynamic methods have potential for both fundamental study of friction and wear and for the development of new (e.g., self-lubricating) materials.
TL;DR: Using a selection of basic vocabulary in nearly one half of the world’s languages, a systematic approach is presented to find commonalities among sound shapes for words referring to same concepts that are interpreted as due to sound symbolism.
Abstract: The relationship between meanings of words and their sound shapes is to a large extent arbitrary, but it is well known that languages exhibit sound symbolism effects violating arbitrariness. Evidence for sound symbolism is typically anecdotal, however. Here we present a systematic approach. Using a selection of basic vocabulary in nearly one half of the world’s languages we find commonalities among sound shapes for words referring to same concepts. These are interpreted as due to sound symbolism. Studying the effects of sound symbolism cross-linguistically is of key importance for the understanding of language evolution.
TL;DR: The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations.
Abstract: The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on five parameters which are: the Prandtl number, the irreversibility coefficients, the inclination angle of the magnetic field, the thermal Grashof and the Hartmann numbers. Effects of these parameters on total and local irreversibilities as well as on heat transfer and fluid flow are studied. It was found that the magnetic field tends to decrease the convection currents, the heat transfer and entropy generation inside the enclosure. Influence of inclination angle of the magnetic field on local irreversibility is then studied.
TL;DR: This paper compares several two-parameter models, including Beta function, Yule function, Weibull function—all can be framed as a multiple regression in the logarithmic scale—in their fitting performance of several ranked linguistic data, such as letter frequencies, word-spacings, and word frequencies.
Abstract: It is well known that many ranked linguistic data can fit well with one-parameter models such as Zipf’s law for ranked word frequencies. However, in cases where discrepancies from the one-parameter model occur (these will come at the two extremes of the rank), it is natural to use one more parameter in the fitting model. In this paper, we compare several two-parameter models, including Beta function, Yule function, Weibull function—all can be framed as a multiple regression in the logarithmic scale—in their fitting performance of several ranked linguistic data, such as letter frequencies, word-spacings, and word frequencies. We observed that Beta function fits the ranked letter frequency the best, Yule function fits the ranked word-spacing distribution the best, and Altmann, Beta, Yule functions all slightly outperform the Zipf’s power-law function in word ranked- frequency distribution.
TL;DR: This article develops a framework for modeling interpersonal alignment in terms of the structural similarity of the interlocutors' dialog lexica by means of so-called two-layer time-aligned network series, that is, a time-adjusted graph model.
Abstract: In dyadic communication, both interlocutors adapt to each other linguistically, that is, they align interpersonally. In this article, we develop a framework for modeling interpersonal alignment in terms of the structural similarity of the interlocutors' dialog lexica. This is done by means of so-called two-layer time-aligned network series, that is, a time-adjusted graph model. The graph model is partitioned into two layers, so that the interlocutors' lexica are captured as subgraphs of an encompassing dialog graph. Each constituent network of the series is updated utterance-wise. Thus, both the inherent bipartition of dyadic conversations and their gradual development are modeled. The notion of alignment is then operationalized within a quantitative model of structure formation based on the mutual information of the subgraphs that represent the interlocutor's dialog lexica. By adapting and further developing several models of complex network theory, we show that dialog lexica evolve as a novel class of graphs that have not been considered before in the area of complex (linguistic) networks. Additionally, we show that our framework allows for classifying dialogs according to their alignment status. To the best of our knowledge, this is the first approach to measuring alignment in communication that explores the similarities of graph-like cognitive representations.
TL;DR: This review presents results obtained from the group’s approach to model quantum mechanics with the aid of nonequilibrium thermodynamics, and it is shown that the exact Schrodinger equation can be derived by assuming that a particle of energy is actually a dissipative system maintained in aNonequilibrium steady state by a constant throughput of energy.
Abstract: This review presents results obtained from our group’s approach to model quantum mechanics with the aid of nonequilibrium thermodynamics. As has been shown, the exact Schrodinger equation can be derived by assuming that a particle of energy is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow). Here, also other typical quantum mechanical features are discussed and shown to be completely understandable within our approach, i.e., on the basis of the assumed sub-quantum thermodynamics. In particular, Planck’s relation for the energy of a particle, the Heisenberg uncertainty relations, the quantum mechanical superposition principle and Born’s rule, or the “dispersion of the Gaussian wave packet”, a.o., are all explained on the basis of purely classical physics.
TL;DR: It is argued that in practical terms the MEP principle should be applied to Earth system processes in terms of the already established framework of non-equilibrium thermodynamics, with the assumption of local thermodynamic equilibrium at the appropriate scales.
Abstract: The Maximum Entropy Production (MEP) principle has been remarkably successful in producing accurate predictions for non-equilibrium states. We argue that this is because the MEP principle is an effective inference procedure that produces the best predictions from the available information. Since all Earth system processes are subject to the conservation of energy, mass and momentum, we argue that in practical terms the MEP principle should be applied to Earth system processes in terms of the already established framework of non-equilibrium thermodynamics, with the assumption of local thermodynamic equilibrium at the appropriate scales.
TL;DR: A new statistical method, closely related to Tsallis entropy, is proposed and shown to be robust for outliers, and a local learning property associated with the method is discussed.
Abstract: In statistical physics, Boltzmann-Shannon entropy provides good understanding for the equilibrium states of a number of phenomena. In statistics, the entropy corresponds to the maximum likelihood method, in which Kullback-Leibler divergence connects Boltzmann-Shannon entropy and the expected log-likelihood function. The maximum likelihood estimation has been supported for the optimal performance, which is known to be easily broken down in the presence of a small degree of model uncertainty. To deal with this problem, a new statistical method, closely related to Tsallis entropy, is proposed and shown to be robust for outliers, and we discuss a local learning property associated with the method.
TL;DR: Thermoeconomics, commonly used for the optimization and diagnosis of energy systems, is proposed as a tool for the characterization of Industrial Ecology by extending the thermoeconomic process of the cost formation of wastes in order to consider their use as input for other processes.
Abstract: Industrial Ecology involves the transformation of industrial processes from linear to closed loop systems: matter and energy flows which were initially considered as wastes become now resources for existing or new processes. In this paper, Thermoeconomics, commonly used for the optimization and diagnosis of energy systems, is proposed as a tool for the characterization of Industrial Ecology. Thermoeconomics is based on the exergy analysis (Thermodynamics) but goes further by introducing the concepts of purpose and cost (Economics). It is presented in this study as a systematic and general approach for the analysis of waste flow integration. The formulation is based on extending the thermoeconomic process of the cost formation of wastes in order to consider their use as input for other processes. Consequently, it can be applied to important Industrial Ecology issues such as identification of integration possibilities and efficiency improvement, quantification of benefits obtained by integration, or determination of fair prices based on physical roots. The capability of the methodology is demonstrated by means of a case study based on the integration of a power plant, a cement kiln and a gas-fired boiler.
TL;DR: How maximum entropy models have been applied to neuronal ensemble data to account for spatial and temporal correlations is reviewed and criticisms of the maximum entropy approach are discussed that argue that it is not generally applicable to larger ensembles of neurons.
Abstract: Understanding how ensembles of neurons collectively interact will be a key step in developing a mechanistic theory of cognitive processes. Recent progress in multineuron recording and analysis techniques has generated tremendous excitement over the physiology of living neural networks. One of the key developments driving this interest is a new class of models based on the principle of maximum entropy. Maximum entropy models have been reported to account for spatial correlation structure in ensembles of neurons recorded from several different types of data. Importantly, these models require only information about the firing rates of individual neurons and their pairwise correlations. If this approach is generally applicable, it would drastically simplify the problem of understanding how neural networks behave. Given the interest in this method, several groups now have worked to extend maximum entropy models to account for temporal correlations. Here, we review how maximum entropy models have been applied to neuronal ensemble data to account for spatial and temporal correlations. We also discuss criticisms of the maximum entropy approach that argue that it is not generally applicable to larger ensembles of neurons. We conclude that future maximum entropy models will need to address three issues: temporal correlations, higher-order correlations, and larger ensemble sizes. Finally, we provide a brief list of topics for future research.
TL;DR: It is argued that Q provides a measure of the imprint of a second-order observing system—a model entertained by the system itself—on the underlying information processing within the information processing.
Abstract: Mutual information among three or more dimensions (μ* = -Q) has been considered as interaction information. However, Krippendorff (1,2) has shown that this measure cannot be interpreted as a unique property of the interactions and has proposed an alternative measure of interaction information based on iterative approximation of maximum entropies. Q can then be considered as a measure of the difference between interaction information and redundancy generated in a model entertained by an observer. I argue that this provides us with a measure of the imprint of a second-order observing system—a model entertained by the system itself—on the underlying information processing. The second-order system communicates meaning hyper-incursively; an observation instantiates this meaning-processing within the information processing. The net results may add to or reduce the prevailing uncertainty. The model is tested empirically for the case where textual organization can be expected to contain intellectual organization in terms of distributions of title words, author names, and cited references.
TL;DR: A comparative analysis of the island constituents of Spanish and English showed that Spanish words in the islands tended to be phonologically and semantically similar to each other, but English wordsIn conclusion, this analysis yielded hypotheses about language processing that can be tested with psycholinguistic experiments, and offer insight into cross-language differences in processing.
Abstract: Previous network analyses of several languages revealed a unique set of structural characteristics. One of these characteristics—the presence of many smaller components (referred to as islands)—was further examined with a comparative analysis of the island constituents. The results showed that Spanish words in the islands tended to be phonologically and semantically similar to each other, but English words in the islands tended only to be phonologically similar to each other. The results of this analysis yielded hypotheses about language processing that can be tested with psycholinguistic experiments, and offer insight into cross-language differences in processing that have been previously observed.
TL;DR: This paper reviews the application of exergy in ecology in the fields of ecological modeling and natural ecosystem monitoring, with special attention paid to the use ofExergy for aquatic ecosystem studies, particularly, assessment of the lake Baikal ecosystem state.
Abstract: Exergy is demonstrated to be a useful measurable parameter reflecting the state of the ecosystem, and allowing estimation of the severity of its anthropogenous damage. Exergy is shown to have advantages such as good theoretical basis in thermodynamics, close relation to information theory, rather high correlation with others ecosystem goal functions and relative ease of computation. Nowadays exergy is often used in ecological assessment. This paper reviews the application of exergy in ecology in the fields of ecological modeling and natural ecosystem monitoring. Special attention is paid to the use of exergy for aquatic ecosystem studies, particularly, assessment of the lake Baikal ecosystem state.
TL;DR: The focus of biosemiotics is shifted from living organisms to agents in general, which all belong to a pragmasphere or functional universe, and a separate classification of signs at the vegetative level that includes proto-icons, proto-indexes, and proto-symbols is considered.
Abstract: Biosemiotics and cybernetics are closely related, yet they are separated by the boundary between life and non-life: biosemiotics is focused on living organisms, whereas cybernetics is applied mostly to non-living artificial devices. However, both classes of systems are agents that perform functions necessary for reaching their goals. I propose to shift the focus of biosemiotics from living organisms to agents in general, which all belong to a pragmasphere or functional universe. Agents should be considered in the context of their hierarchy and origin because their semiosis can be inherited or induced by higher-level agents. To preserve and disseminate their functions, agents use functional information - a set of signs that encode and control their functions. It includes stable memory signs, transient messengers, and natural signs. The origin and evolution of functional information is discussed in terms of transitions between vegetative, animal, and social levels of semiosis, defined by Kull. Vegetative semiosis differs substantially from higher levels of semiosis, because signs are recognized and interpreted via direct code-based matching and are not associated with ideal representations of objects. Thus, I consider a separate classification of signs at the vegetative level that includes proto-icons, proto-indexes, and proto-symbols. Animal and social semiosis are based on classification, and modeling of objects, which represent the knowledge of agents about their body (Innenwelt) and environment (Umwelt).
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TL;DR: In this article, the authors present tools which could be helpful for the treatment of convex roof extensions in quantum information theory, and describe the Wootters method, the subtraction procedure, and examples on how to use symmetries.
Abstract: Convex roof extensions are widely used to create entanglement measures in quantum information theory. The aim of the article is to present some tools which could be helpful for their treatment. Sections 2 and 3 introduce into the subject. It follows descriptions of the Wootters' method, of the "subtraction procedure", and examples on how to use symmetries.
TL;DR: It is shown that a higher number of interrelated processes within the system result in an increased probability of self-organization, which is confirmed by the investigation of the wear performance of a novel Ti0.1N (PVD) coating with complex nano-multilayered structure under extreme tribological conditions of dry high-speed end milling of hardened H13 tool steel.
Abstract: Self-organization during friction in complex surface engineered tribosystems is investigated. The probability of self-organization in these complex tribosystems is studied on the basis of the theoretical concepts of irreversible thermodynamics. It is shown that a higher number of interrelated processes within the system result in an increased probability of self-organization. The results of this thermodynamic model are confirmed by the investigation of the wear performance of a novel Ti0.2Al0.55Cr0.2Si0.03Y0.02N/Ti0.25Al0.65Cr0.1N (PVD) coating with complex nano-multilayered structure under extreme tribological conditions of dry high-speed end milling of hardened H13 tool steel.
TL;DR: The structural properties of chemical reaction systems obeying the mass action law are investigated and related to the physical and chemical properties of the system and an entropy-based Lyapunov function candidate serves as a tool for proving structural stability.
Abstract: In this paper, the structural properties of chemical reaction systems obeying the mass action law are investigated and related to the physical and chemical properties of the system. An entropy-based Lyapunov function candidate serves as a tool for proving structural stability, the existence of which is guaranteed by the second law of thermodynamics. The commonly used engineering model reduction methods, the so-called quasi equilibrium and quasi steady state assumption based reductions, together with the variable lumping are formally defined as model transformations acting on the reaction graph. These model reduction transformations are analysed to find conditions when (a) the reduced model remains in the same reaction kinetic system class, (b) the reduced model retains the most important properties of the original one including structural stability. It is shown that both variable lumping and quasi equilibrium based reduction preserve both the reaction kinetic form and the structural stability of reaction kinetic models of closed systems with mass action law kinetics, but this is not always the case for the reduction based on quasi steady state assumption.
TL;DR: Compared to traditional white noise testing which depends on “autocorrelations”, the proposed method uses energy distributions to distinguish real signals and noise in noisy series, therefore the chosen DL is reliable, and the WTD results of time series can be improved.
Abstract: In this paper, the energy distributions of various noises following normal, log-normal and Pearson-III distributions are first described quantitatively using the wavelet energy entropy (WEE), and the results are compared and discussed. Then, on the basis of these analytic results, a method for use in choosing the decomposition level (DL) in wavelet threshold de-noising (WTD) is put forward. Finally, the performance of the proposed method is verified by analysis of both synthetic and observed series. Analytic results indicate that the proposed method is easy to operate and suitable for various signals. Moreover, contrary to traditional white noise testing which depends on “autocorrelations”, the proposed method uses energy distributions to distinguish real signals and noise in noisy series, therefore the chosen DL is reliable, and the WTD results of time series can be improved.
TL;DR: It is shown that superstatistics is a special case of an integral transform, and thus can be understood as a particular way in which to change the scale of measurement, and incorporation of information about measurement scale into maximum entropy provides a general approach to the relations between measurement, information and probability.
Abstract: We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use measurement scale as a type of information constraint. We argue that a very common measurement scale is linear at small magnitudes grading into logarithmic at large magnitudes, leading to observations that often follow Student's probability distribution which has a Gaussian shape for small fluctuations from the mean and a power law shape for large fluctuations from the mean. An inverse scaling often arises in which measures naturally grade from logarithmic to linear as one moves from small to large magnitudes, leading to observations that often follow a gamma probability distribution. A gamma distribution has a power law shape for small magnitudes and an exponential shape for large magnitudes. The two measurement scales are natural inverses connected by the Laplace integral transform. This inversion connects the two major scaling patterns commonly found in nature. We also show that superstatistics is a special case of an integral transform, and thus can be understood as a particular way in which to change the scale of measurement. Incorporating information about measurement scale into maximum entropy provides a general approach to the relations between measurement, information and probability.
TL;DR: By examining this network of feedback loops for seven ecosystems in different climate regions, it is found that the feedback tends to maximize information production in the entire system, and the latter increases with increasing variability within the whole system.
Abstract: Variability plays an important role in the self-organized interaction between vegetation and its environment, yet the principles that characterize the role of the variability in these interactions remain elusive. To address this problem, we study the dependence between a number of variables measured at flux towers by quantifying the information flow between the different variables along with the associated time lag. By examining this network of feedback loops for seven ecosystems in different climate regions, we find that: (1) the feedback tends to maximize information production in the entire system, and the latter increases with increasing variability within the whole system; and (2) variables that participate in feedback exhibit moderated variability. Self-organization arises as a tradeoff where the ability of the total system to maximize information production through feedback is limited by moderate variability of the participating variables. This relationship between variability and information production leads to the emergence of ordered organization.