Brillouin Science And Information Theory Pdf To Jpg

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306 CHAPTER 7. COLOR AND GRAPHICS tothepublic,muchlessapayingclient.Designers,ontheotherhand,havetodojustthat{articulateanddefendtheircolorchoicesanditsmerits. How do I combine two or more images to get a single pdf file? In Lion, how can I efficiently combine 10 jpeg files into a single pdf in which each image is a page? I have preview. Mar 17, 2013  Obviously, the most important concept of Shannon’s information theory is information. Although we all seem to have an idea of what information is, it’s nearly impossible to define it clearly. And, surely enough, the definition given by Shannon seems to come out of nowhere.

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?[1] Later, Léon Brillouin shortened the phrase to negentropy.[2][3] 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.

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

“[..] if 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.”

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.[4] 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.

Information theory[edit]

In information theory and statistics, negentropy is used as a measure of distance to normality.[5][6][7] 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.

Negentropy is defined as

J(px)=S(φx)−S(px){displaystyle J(p_{x})=S(varphi _{x})-S(p_{x}),}

where S(φx){displaystyle S(varphi _{x})} is the differential entropy of the Gaussian density with the same mean and variance as px{displaystyle p_{x}} and S(px){displaystyle S(p_{x})} is the differential entropy of px{displaystyle p_{x}}:

S(px)=−∫px(u)log⁡px(u)du{displaystyle 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.[8][9]

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Correlation between statistical negentropy and Gibbs' free energy[edit]

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 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 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.[10] In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. 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 process[11][12][13] (both quantities differs just with a figure sign) and then Planck for the isothermal-isobaric process.[14] 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,[15] applied among the others in molecular biology[16] and thermodynamic non-equilibrium processes.[17]

J=Smax−S=−Φ=−kln⁡Z{displaystyle J=S_{max }-S=-Phi =-kln Z,}
where:
S{displaystyle S} is entropy
J{displaystyle J} is negentropy (Gibbs 'capacity for entropy')
Φ{displaystyle Phi } is the Massieu potential
Z{displaystyle Z} is the partition function
k{displaystyle k} the Boltzmann constant

Brillouin's negentropy principle of information[edit]

In 1953, Léon Brillouin derived a general equation[18] 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,[19] 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.

See also[edit]

Notes[edit]

  1. ^Schrödinger, Erwin, What is Life – the Physical Aspect of the Living Cell, Cambridge University Press, 1944
  2. ^Brillouin, Leon: (1953) 'Negentropy Principle of Information', J. of Applied Physics, v. 24(9), pp. 1152–1163
  3. ^Léon Brillouin, La science et la théorie de l'information, Masson, 1959
  4. ^Mahulikar, S.P. & Herwig, H.: (2009) 'Exact thermodynamic principles for dynamic order existence and evolution in chaos', Chaos, Solitons & Fractals, v. 41(4), pp. 1939–1948
  5. ^Aapo Hyvärinen, Survey on Independent Component Analysis, node32: Negentropy, Helsinki University of Technology Laboratory of Computer and Information Science
  6. ^Aapo Hyvärinen and Erkki Oja, Independent Component Analysis: A Tutorial, node14: Negentropy, Helsinki University of Technology Laboratory of Computer and Information Science
  7. ^Ruye Wang, Independent Component Analysis, node4: Measures of Non-Gaussianity
  8. ^P. Comon, Independent Component Analysis – a new concept?, Signal Processing, 36 287–314, 1994.
  9. ^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.
  10. ^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)
  11. ^Massieu, M. F. (1869a). Sur les fonctions caractéristiques des divers fluides. C. R. Acad. Sci. LXIX:858–862.
  12. ^Massieu, M. F. (1869b). Addition au precedent memoire sur les fonctions caractéristiques. C. R. Acad. Sci. LXIX:1057–1061.
  13. ^Massieu, M. F. (1869), Compt. Rend.69 (858): 1057.
  14. ^Planck, M. (1945). Treatise on Thermodynamics. Dover, New York.
  15. ^Antoni Planes, Eduard Vives, Entropic Formulation of Statistical Mechanics, Entropic variables and Massieu–Planck functions 2000-10-24 Universitat de Barcelona
  16. ^John A. Scheilman, Temperature, Stability, and the Hydrophobic Interaction, Biophysical Journal73 (December 1997), 2960–2964, Institute of Molecular Biology, University of Oregon, Eugene, Oregon 97403 USA
  17. ^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
  18. ^Leon Brillouin, The negentropy principle of information, J. Applied Physics24, 1152–1163 1953
  19. ^Leon Brillouin, Science and Information theory, Dover, 1956
Look up negentropy in Wiktionary, the free dictionary.
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Negentropy&oldid=883292901'

Introduction

Brillouin Science And Information Theory Pdf To Jpg Converter

Fine ferromagnetic particles of a nanometer-scale size have important applications in various fields of modern nanotechnology, such as magnetic recording, permanent magnet industry, biomedical applications, etc. [1]. The continuum theory of micromagnetism, which was developed in the 1930s and 1940s, was intended to bridge the gap between the phenomenological Maxwell's theory of electromagnetic fields and quantum theory based on atomic backgrounds. In Maxwell's theory, material properties are described using global permeabilities and susceptibilities valid for macroscopic dimensions. On the other hand, quantum theory allows a description of magnetic properties on the atomistic level. A modern theory of micromagnetism has been born by Brown's attempt to explain the so far unexplained 1/H term in the law of approach to ferromagnetic saturation. The breakthrough toward a continuum theory of magnetism is due to Landau and Lifshitz (1935), who derived a continuum expression for the exchange energy and gave a first interpretation of domain patterns [2]. Ferromagnetic materials consist of small volumes of solid called magnetic domains in which atomic magnetic dipole moments of about 1012 to 1015 atoms align parallel to each other spontaneously. The emergence of magnetization M may be due to a change in magnetic field strength H. Hysteresis loop proceeds in three main stages: initial reversible magnetization, rapid irreversible magnetization, and the slow approach to saturation, which they related, respectively, to the reversible shifts of domain walls, irreversible rotation and shift processes, and the reversible rotation of domains [3].

These stages are being visible in the insets of Figures 1, 2, 3, and 4. Much effort is being undertaken by different scientists in order to describe all magnetization curves. Mathematical approximations are given by the multicomponent exponential or sine-series functions [4]. Some other approximations result from the general descriptions of hysteresis, such as the Preisach [5], Jiles-Atherton [6], Takacs [7], and Akulov [8] models. Moreover, it is unlikely that any one theory can be developed that will apply to all materials.

Brillouin Science And Information Theory Pdf To Jpg Online

It is usually taken for granted that the Brillouin function might describe the magnetization curves of many magnetic materials. In this work, an attempt to find an approximation based on the Brillouin function is undertaken. For this purpose, the following assumptions are made:

Brillouin Science And Information Theory Pdf To Jpg

  1. 1.

    The description should have a phenomenological background.

  2. 2.

    Its parameters should have a physical meaning.

  3. 3.

    The modified Brillouin function, chosen for modeling, should be verified using experimental data.

  4. 4.

    It is expected to achieve high accuracy in the region of wide range of magnetization changes.

Brillouin Science And Information Theory Pdf To Jpg Free

For these purposes, the experimental data of α-Fe2O3 nanoparticles have been utilized such that their magnetization results were measured by vibrating sample magnetization (VSM). Sweet valley eternal champ zip.

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