In information theory and statistics, negentropy is used as a measure of distance to normality.Aapo Hyvärinen, Survey on Independent Component Analysis, node32: Negentropy, Helsinki University of Technology Laboratory of Computer and Information ScienceAapo Hyvärinen and Erkki Oja, Independent Component Analysis: A Tutorial, node14: Negentropy, Helsinki University of Technology Laboratory of Computer and Information ScienceRuye Wang, Independent Component Analysis, node4: Measures of Non-Gaussianity Out of all distributions with a given mean and variance, the normal or Gaussian distribution is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same mean and variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian.
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During the energy exchange, the organism strives to maintain its characteristic order (negentropy) and projects that order onto the surroundings. Due to that, the order of the surroundings is destroyed. By contrast, inanimate matter does not have the ability to maintain or lower its negentropy, because spontaneous natural processes are always accompanied by entropy generation.
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24(9), pp. 1152–1163Léon Brillouin, La science et la théorie de l'information, Masson, 1959 In 1974, Albert Szent- Györgyi proposed replacing the term negentropy with syntropy. That term may have originated in the 1940s with the Italian mathematician Luigi Fantappiè, who tried to construct a unified theory of biology and physics. Buckminster Fuller tried to popularize this usage, but negentropy remains common.
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In information theory and statistics, negentropy is used as a measure of distance to normality. The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his 1944 popular-science book What is Life?Schrödinger, Erwin, What is Life – the Physical Aspect of the Living Cell, Cambridge University Press, 1944 Later, Léon Brillouin shortened the phrase to negentropy.Brillouin, Leon: (1953) "Negentropy Principle of Information", J. of Applied Physics, v.
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41(4), pp. 1939–1948 Thus, negentropy has SI units of (J kg−1 K−1) when defined based on specific entropy per unit mass, and (K−1) when defined based on specific entropy per unit energy. This definition enabled: i) scale-invariant thermodynamic representation of dynamic order existence, ii) formulation of physical principles exclusively for dynamic order existence and evolution, and iii) mathematical interpretation of Schrödinger's negentropy debt.
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Negentropy is defined as :J(p_x) = S(\varphi_x) - S(p_x)\, where S(\varphi_x) is the differential entropy of the Gaussian density with the same mean and variance as p_x and S(p_x) is the differential entropy of p_x: :S(p_x) = - \int p_x(u) \log p_x(u) \, du Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in independent component analysis.P. Comon, Independent Component Analysis – a new concept?, Signal Processing, 36 287–314, 1994.
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Synergetics refers to synergy: either the concept of the output of a system not foreseen by the simple sum of the output of each system part, or simply -- less used -- another term for negative entropy -- negentropy.
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It corresponds exactly to the definition of negentropy adopted in statistics and information theory. A similar physical quantity was introduced in 1869 by Massieu for the isothermal processMassieu, M. F. (1869a). Sur les fonctions caractéristiques des divers fluides.
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Struzik proposed that information metabolism theory may be used as an extension to Brillouin's negentropy principle of information. Inspired by Kępiński's work and Jungian typology, Augustinavičiūtė proposed her theory of information metabolism in human mind and society, known as Socionics.
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In a brute force search for a randomly generated password, the entropy of the unknown string can be effectively reduced by a similar amount. Because the negentropy and computational power diverge as the noise term goes to zero, complexity class may not be the best way to describe the capabilities of time machines.
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First edition (publ. Basic Books) Out of Control: The New Biology of Machines, Social Systems, and the Economic World () is a 1992 book by Kevin Kelly. Major themes in Out of Control are cybernetics, emergence, self-organization, complex systems, negentropy and chaos theory and it can be seen as a work of techno-utopianism.
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His wife Marcelle died in 1986. Brillouin was a founder of modern solid state physics for which he discovered, among other things, Brillouin zones. He applied information theory to physics and the design of computers and coined the concept of negentropy to demonstrate the similarity between entropy and information. Brillouin offered a solution to the problem of Maxwell's demon.
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In a note to What is Life? Schrödinger explained his use of this phrase. In 2009, Mahulikar & Herwig redefined negentropy of a dynamically ordered sub-system as the specific entropy deficit of the ordered sub-system relative to its surrounding chaos.Mahulikar, S.P. & Herwig, H.: (2009) "Exact thermodynamic principles for dynamic order existence and evolution in chaos", Chaos, Solitons & Fractals, v.
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Even if a clone with the same organizational principle (e.g. identical DNA-structure) could be developed, this would not mean that the former distinct system comes back into being. Events to which the self-organizing capacities of organisms, species or other complex systems can adapt, like minor injuries or changes in the physical environment are reversible. However, adaptation depends on import of negentropy into the organism, thereby increasing irreversible processes in its environment.
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Information metabolism is a psychological theory of interaction between biological organisms and their environment based on information processing. The most detailed description of information metabolism concept was given by Kępiński in his book Melancholy (1974). In this model, the living organism is considered an open system as understood by von Bertalanffy. Living beings are characterized by ability to increase and maintain their own negentropy - an idea popularized in Schrödinger's book What is life?.
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After Szent-Györgyi commented on his financial hardships in a 1971 newspaper interview, attorney Franklin Salisbury contacted him and later helped him establish a private nonprofit organization, the National Foundation for Cancer Research. Late in life, Szent-Györgyi began to pursue free radicals as a potential cause of cancer. He came to see cancer as being ultimately an electronic problem at the molecular level. In 1974, reflecting his interests in quantum physics, he proposed the term "syntropy" replace the term "negentropy".
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A related description of CTC physics was given in 2001 by Michael Devin, and applied to thermodynamics. The same model with the introduction of a noise term allowing for inexact periodicity, allows the grandfather paradox to be resolved, and clarifies the computational power of a time machine assisted computer. Each time traveling qubit has an associated negentropy, given approximately by the logarithm of the noise of the communication channel. Each use of the time machine can be used to extract as much work from a thermal bath.
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Treatise on Thermodynamics. Dover, New York. More recently, the Massieu–Planck thermodynamic potential, known also as free entropy, has been shown to play a great role in the so-called entropic formulation of statistical mechanics,Antoni Planes, Eduard Vives, Entropic Formulation of Statistical Mechanics, Entropic variables and Massieu–Planck functions 2000-10-24 Universitat de Barcelona applied among the others in molecular biologyJohn A. Scheilman, Temperature, Stability, and the Hydrophobic Interaction, Biophysical Journal 73 (December 1997), 2960–2964, Institute of Molecular Biology, University of Oregon, Eugene, Oregon 97403 USA and thermodynamic non-equilibrium processes.Z. Hens and X. de Hemptinne, Non- equilibrium Thermodynamics approach to Transport Processes in Gas Mixtures, Department of Chemistry, Catholic University of Leuven, Celestijnenlaan 200 F, B-3001 Heverlee, Belgium :: J = S_\max - S = -\Phi = -k \ln Z\, ::where: ::S is entropy ::J is negentropy (Gibbs "capacity for entropy") ::\Phi is the Massieu potential ::Z is the partition function ::k the Boltzmann constant In particular, mathematically the negentropy (the negative entropy function, in physics interpreted as free entropy) is the convex conjugate of LogSumExp (in physics interpreted as the free energy).
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Didier G. Leibovici and Christian Beckmann, An introduction to Multiway Methods for Multi-Subject fMRI experiment, FMRIB Technical Report 2001, Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB), Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital, Headley Way, Headington, Oxford, UK. The negentropy of a distribution is equal to the Kullback–Leibler divergence between p_x and a Gaussian distribution with the same mean and variance as p_x (see Differential entropy#Maximization in the normal distribution for a proof). In particular, it is always nonnegative.
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In 1953, Léon Brillouin derived a general equationLeon Brillouin, The negentropy principle of information, J. Applied Physics 24, 1152–1163 1953 stating that the changing of an information bit value requires at least kT ln(2) energy. This is the same energy as the work Leó Szilárd's engine produces in the idealistic case. In his book,Leon Brillouin, Science and Information theory, Dover, 1956 he further explored this problem concluding that any cause of this bit value change (measurement, decision about a yes/no question, erasure, display, etc.) will require the same amount of energy.
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ICA finds the independent components (also called factors, latent variables or sources) by maximizing the statistical independence of the estimated components. We may choose one of many ways to define a proxy for independence, and this choice governs the form of the ICA algorithm. The two broadest definitions of independence for ICA are # Minimization of mutual information # Maximization of non-Gaussianity The Minimization-of-Mutual information (MMI) family of ICA algorithms uses measures like Kullback-Leibler Divergence and maximum entropy. The non-Gaussianity family of ICA algorithms, motivated by the central limit theorem, uses kurtosis and negentropy.
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The 1944 book What is Life? by Nobel-laureate physicist Erwin Schrödinger stimulated further research in the field. In his book, Schrödinger originally stated that life feeds on negative entropy, or negentropy as it is sometimes called, but in a later edition corrected himself in response to complaints and stated that the true source is free energy. More recent work has restricted the discussion to Gibbs free energy because biological processes on Earth normally occur at a constant temperature and pressure, such as in the atmosphere or at the bottom of the ocean, but not across both over short periods of time for individual organisms.
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The idea was continued by Struzik, who proposed that Kępiński's information metabolism theory may be seen as an extension of Léon Brillouin's negentropy principle of information. In 2011, the notion of "psychological entropy" was reintroduced to psychologists by Hirsh et al. Similarly to Kępiński, these authors noted that uncertainty management is a critical ability for any organism. Uncertainty, arising due to the conflict between competing perceptual and behavioral affordances, is experienced subjectively as anxiety. Hirsh and his collaborators proposed that both the perceptual and behavioral domains may be conceptualized as probability distributions and that the amount of uncertainty associated with a given perceptual or behavioral experience can be quantified in terms of Claude Shannon’s entropy formula.
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There is a physical quantity closely linked to free energy (free enthalpy), with a unit of entropy and isomorphic to negentropy known in statistics and information theory. In 1873, Willard Gibbs created a diagram illustrating the concept of free energy corresponding to free enthalpy. On the diagram one can see the quantity called capacity for entropy. This quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume.Willard Gibbs, A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces, Transactions of the Connecticut Academy, 382–404 (1873) In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy.
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