Negentropy

Negative entropy or negentropy or syntropy of a living system is the entropy that it exports to maintain its own entropy low (see entropy and life). The concept and phrase were introduced by Erwin Schrödinger in his 1943 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. 24:9, pp. 1152-1163 Léon Brillouin La science et la théorie de l\'information, Masson, 1959 to express it in a more "positive" way: a living system imports negentropy and stores it.Mae-Wan Ho, What is (Schrödinger\'s) Negentropy?, Bioelectrodynamics Laboratory, Open university Walton Hall, Milton Keynes 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. (This attempt has not gained renown or borne great fruit.) Buckminster Fuller tried to popularize this usage, but negentropy remains common.

In a note to What is Life? Schrödinger explained his use of this phrase.

“

[I]f I had been catering for them [physicists] alone I should have let the discussion turn on free energy instead. It is the more familiar notion in this context. But this highly technical term seemed linguistically too near to energy for making the average reader alive to the contrast between the two things.

”

Contents 1 Information theory 2 Correlation between statistical negentropy and Gibbs\' free energy 3 Organization theory 4 Notes 5 See also

Information theory

In information theory and statistics, negentropy is used as a measure of distance to normality. http://www.cis.hut.fi/aapo/papers/NCS99web/node32.html Aapo Hyvärinen, Survey on Independent Component Analysis, node32: Negentropy, Helsinki University of Technology Laboratory of Computer and Information Sciencehttp://www.cis.hut.fi/aapo/papers/IJCNN99_tutorialweb/node14.html Aapo 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 Consider a signal with a certain distribution. If the signal is Gaussian, the signal is said to have a normal distribution. Negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes iff the signal is Gaussian.

Negentropy is defined as

$J(p\_x)\; =\; S(\backslash phi\_x)\; -\; S(p\_x)\backslash ,$

where $S(\backslash phi\_x)$ stands for the Gaussian density with the same mean and variance as $p\_x$ and $S(p\_x)$ is the differential entropy:

$S(p\_x)\; =\; -\; \backslash int\; p\_x(u)\; \backslash log\; p\_x(u)\; du$

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.http://www.fmrib.ox.ac.uk/analysis/techrep/tr01dl1/tr01dl1/tr01dl1.html Didier G. Leibovici and Christian Beckmann, An introduction to Multiway Methods for Multi-Subject fMRI experiment. FMRIB Technical Report, 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. Negentropy can be understood intuitively as the information that can be saved when representing $p\_x$ in an efficient way; if $p\_x$ where a random variable (with Gaussian distribution) with the same mean and variance, would need the maximum length of data to be represented, even in the most efficient way. Since $p\_x$ is less random, then something about it is known beforehand, it contains less unknown information, and needs less length of data to be represented in an efficient way.

Correlation between statistical negentropy and Gibbs\' free energy

Willard Gibbs’ 1873 available energy (free energy) graph, which shows a plane perpendicular to the axis of v (volume) and passing through point A, which represents the initial state of the body. MN is the section of the surface of dissipated energy. Qε and Qη are sections of the planes η = 0 and ε = 0, and therefore parallel to the axes of ε (internal energy) and η (entropy) respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its available energy (Gibbs free energy) and its capacity for entropy (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume) respectively.

There is a physical quantity closely linked to free energy (free enthalpy), with a unit of entropy and isomorfic to negentropy known in statistics and information theory. In 1873 Willard Gibbs created a diagram illustrating concept of free energy corresponding to free enthalpy . On the diagram one can see the quantity called capacity for entropy. The said quantity is amount of entropy that may be increased without changing an internal energy or increasing its volume. http://www.ufn.ru/ufn39/ufn39_4/Russian/r394b.pdf 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. It corresponds exactly to adopted in statistics and theory information, definition of negentropy. Similar physical quantity introduced in 1869 Massieu for isothermal process Massieu, M. F. 1869a. Sur les fonctions caract6ristiques des divers fluides. C. R. Acad. Sci. LXIX:858-862.Massieu, M. F. 1869b. Addition au precedent memoire sur les fonctions caract6ristiques. C. R. Acad. Sci. LXIX:1057-1061.Massieu, M. F. (1869), "Compt. Rend." 69 (858): 1057. (both quantities differs just with a figure sign) and than Planck for the isothermal-isobaric process Planck, M. 1945. Treatise on Thermodynamics. Dover, New York. Recently, Massieu-Planck thermodynamic potential, known also as free entropy, plays a great role in 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 biology.http://www.biophysj.org/cgi/reprint/73/6/2960.pdf John A. Scheilman, Temperature, Stability, and the Hydrophobic Interaction, Biophysical Journal Volume 73 December 1997 2960-2964, Institute of Molecular Biology, University of Oregon, Eugene, Oregon 97403 USA and thermodynamic non-equilibriumi processes. http://arxiv.org/pdf/chao-dyn/9604008 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

$J\; =\; S\_\backslash max\; -\; S\; =\; -\backslash Phi\; =\; -k\; \backslash ln\; Z\backslash ,$

where:

$J$ - negentropy (Gibbs "capacity for entropy")

$\backslash Phi$ – Massieu potential

$Z$ - partition function

$k$ - Boltzmann constant

Organization theory

In risk management, negentropy is the force that seeks to achieve effective organizational behavior and lead to a steady predictable state.Pedagogical Risk and Governmentality: Shantytowns in Argentina in the 21st Century (see p. 4).

Notes

See also

• Ectropy
• Exformation
• Extropy
• Free entropy
• Entropy in thermodynamics and information theory
• Entropy and life

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