General theory of Entropy

Il s’agit de décrire de façon stochastique (c'est-à-dire à partir de matrices utilisées en chaîne de Markov) les lois qui régissent la physique quantique. On veut prouver que de manière théorique, un système quantique peut se stabiliser (en utilisant la propriété de la convergence vue ci-dessus) comme dans un système thermodynamique.

Este é um curso introdutório sobre a Teoria da Informação (Shannon theory) destinado aos estudantes de graduação em Estatística, ministrado no Centro de Ciências Exatas e da Natureza (CCEN) da Universidade Federal de Pernambuco, Recife. Grosso modo, trata-se de uma tentativa de fornecer uma janela panorâmica focada em algumas das técnicas clássicas do assunto, apresentar resultados e as linhas gerais sobre algumas das aplicações desta potente teoria, através de uma seleção particular de tópicos. O conteúdo está longe de ser razoavelmente integralizado: mesmo alguns assuntos como criptografia ou teoria da distorção da taxa sequer foram tratados. O ponto mais relevante a destacar nesta apresentação, a fim de não causar expectativas frustradas ou má interpretação, é que a abordagem não é bem sintonizada com aquela corriqueira na Estatística (correlata com o rigor exigido na Matemática). Com uma formação de Engenharia, a visão adotada permite omitir muitas das provas, e não haver uma preocupação maior com o rigor. Cursos e livros de Teoria da Informação por Matemáticos e/ou Estatísticos costumam ser "um pouco áridos", densos e rigorosos, perdendo-se no formalismo-com ênfase menor no significado, ou em interpretações. O objetivo é um compêndio exordial apresentando a área aos principiantes. Há um espaço particular para tal enfoque: espera-se que os usuários possam aproveitar ou até mesmo apreciar. Bom uso, !

I propose a model wherein a system is represented by a finite sequence of natural numbers. These numbers are thought of as population numbers in statistical ensemble formed as a sample with replacement of entities (microstates) from some abstract set. I derive the concepts of energy and of temperature. I show an analogy between energy spectra computed from the model and energy spectra of some known constructs, such as particle in a box and quantum harmonic oscillator. The presented model replaces the concept of wave function with knowledge vector. I derive Schrödinger-type equation for knowledge vector and discuss principal differences with Schrödinger equation. The model retains major QM hallmarks such as wave-particle duality, violation of Bell’s inequalities, quantum Zeno effect, uncertainty relations, while avoiding controversial concept of wave function collapse. Unlike standard QM and Newtonian mechanics, the presented model has the Second Law of Thermodynamics built-in; in particular, it is not invariant with respect to time reversal.

Edge detection and feature extraction are widely used in image processing and computer vision applications. Most of the traditional methods for edge detection are based on the first and second order derivatives of gray levels of the pixels of the original image utilizing 2D spatial convolution masks to approximate the derivative. In this paper we present an algorithm for edge detection in gray level images.....

Image fusion is to reduce uncertainty and minimize redundancy in the output while maximizing relevant information from two or more images of a scene into a single composite image that is more informative and is more suitable for visual perception or processing tasks like medical imaging, remote sensing, concealed weapon detection, weather forecasting, biometrics etc. Image fusion combines registered images to produce a high quality fused image with spatial and spectral information. The fused image with more information will improve the performance of image analysis algorithms used in different applications. In this paper, we proposed a fuzzy logic method to fuse images from different sensors, in order to enhance the quality and compared proposed method with two other methods i.e. image fusion using wavelet transform and weighted average discrete wavelet transform based image fusion using genetic algorithm (here onwards abbreviated as GA) along with quality evaluation parameters image quality index (IQI), mutual information measure (MIM), root mean square error (RMSE), peak signal to noise ratio (PSNR), fusion factor (FF), fusion symmetry (FS) and fusion index (FI) and entropy. The results obtained from proposed fuzzy based image fusion approach improves quality of fused image as compared to earlier reported methods, wavelet transform based image fusion and weighted average discrete wavelet transform based image fusion using genetic algorithm. KEYWORDS image fusion, wavelet transform, genetic algorithm, fuzzy logic, image quality index, mutual information measure, fusion factor, fusion symmetry, fusion index, entropy.

Inhaltsverzeichnis

1. Kap 1.1 Laser...........................................................................................................................2
2. Kap 1.2 Modenamplituden ...............................................................................................2
3. Kap 3 Wahrscheinlichkeit ...............................................................................................2
4. Kap 3.5 Die Abhängigkeit der Entropie von der Zeit .......................................................2
5. Kap 3.6 Die Liouville Gleichung ........................................................................................... 3 6. Kap 4.1 Wahrscheinlichkeitsdichte und Normalverteilung .......................................4
7. Kap 4.6 Das Prinzip der detaillierten Bilanz ...............................................................4
8. Kap 4.10 Irreversibler Prozess .......................................................................................4
9. Kap 4.11 Irreversible Thermodynamik .......................................................................4

10. Kap 5.1 Der anharmonische Oszillator .......................................................................4
11. Kap 5.4 Die Bifurkation ...............................................................................................5
12. Kap 5.5 Die Katastrophenmenge ...............................................................................6
13. Kap 6.1 Das Dissipations-Fluktuations-Theorem ......................................................... 6
14. Kap 6.7 Der Phasenübergang zweiter Ordnung .......................................................6
15. Kap 7.1 Die adiabatische Näherung ...............................................................................7
16. Kap 7.2 Versklavung ........................................................................................................7
17. Kap 7.3 Fluktuationen und Potentiale .......................................................................7
18. Kap 7.7 Ungedämpfte Moden .......................................................................................8
19. Kap 8.1 Selbstorganisation .......................................................................................8
20. Kap 8.4 Kohärentes Laserlicht .......................................................................................9
21. Kap 8.7.3 Der Einmodenlaser .......................................................................................9
22. Kap 8.8 Das Taylorproblem .......................................................................................9

23. Kap 8.12 Symmetriebrechung ....................................................................................10
24. Kap 8.14 Instabilitätspunkte ....................................................................................10
25. Kap 9.8 Netzwerktheorie ............................................................................................10
26. Kap 10.2 Trajektorien ....................................................................................................10
27. Kap 10.3 Auftreten neuer Arten ............................................................................11
28. Kap 10.4 Das Nervennetzwerk ....................................................................................11
29. Kap 10.5 Die Diffusionskonstante ............................................................................11
30. Kap 10.6 Modellbildung in der Morphogenese: Physikalisches und Biologisches      System .....................................................................................................................................11
31. Kap 11.1 Das Ising Modell ............................................................................................12
32. Kap 11.2 Lokale und allgemeine Phänomene ...................................................13
33. Kap 11.3 Wirtschaftsvorgänge, Technische Neuerungen, Innovationen ...........13
34. Kap 12.1 Chaos ............................................................................................................15
35. Kap 12.4 Die Lorenz Gleichungen ............................................................................15
36. Kap 12.5 Chaotische Bewegung ............................................................................16
37. Kap 12.6 Advanced Synergetics ............................................................................16
38. Kap 13 Analogien zwischen völlig verschiedenen Systemen ............................16

Ein System, das auf der Grenzlinie zwischen natürlichem System und von Menschenhand gemachtem Apparat liegt, ist der Laser. Wir behandeln den Laser, als Apparat, obwohl das Auftreten von Lasertätigkeit (im Mikrowellenbereich) auch im interstellaren Raum beobachtet wurde.

Kap. 1.2 Die erste Klasse der Beispiele bezog sich auf abgeschlossene Systeme. Daraus, sowie aus einer Vielzahl anderer Beispiele, schließt die Thermodynamik, dass die Entropie in abgeschlossenen Systemen niemals abnimmt. Dieses Theorem zu beweisen ist Aufgabe der statistischen Mechanik. Immerhin beleuchtet es das erste Grundproblem bei vielkomponentigen Systemen: Wie sieht eine adäquate Beschreibung in makroskopischen Begriffen aus oder, in welchen Moden wird das System arbeiten? Der Grund liegt in der Linearität der entsprechenden Bewegungsgleichungen, die dazu führt, dass irgendeine Superposition von Lösungen wieder eine Lösung dieser Gleichungen darstellt. Es wird sich herausstellen, dass die Gleichungen, die die Selbstorganisation regieren, nichtlinear sind.

Anstatt alle atomaren Koordinaten von sehr vielen Freiheitsgraden zu kennen, benötigen wir nur einen einzigen oder sehr wenige Parameter, z.B. die Amplitude einer Mode. Wie wir später sehen werden, bestimmen die Modenamplituden die Art und den Grad der Ordnung. Aufgrund dieser Tatsache werden wir sie als Ordnungsparameter bezeichnen und eine Verbindung zur Idee der Ordnungsparameter bei Phasenübergängen herstellen. Das Modenkonzept schließt eine Skalierungseigenschaft ein.

Raumzeitliche Muster können ähnlich sein, unterschiedlich bloß durch die Ausdehnung (Skala) der Amplitude. (Im Übrigen spielt dieses " Ähnlichkeitsprinzip " eine wichtige Rolle bei der Mustererkennung im Gehirn. Allerdings ist bisher kein Mechanismus bekannt, der dies erklären könnte. So wird beispielsweise ein Dreieck als solches erkannt, unabhängig von seiner Ausdehnung (Größe) und Lage).
Kap. 3 In diesem Kapitel wollen wir aufzeigen, wie wir durch eine gewisse Neuinterpretation der Wahrscheinlichkeit in eine scheinbar völlig verschiedene Disziplin, die Informationstheorie nämlich, Einblick gewinnen können.

Kap. 3.5 Da wir Prozesse untersuchen wollen, lassen wir jetzt zu, daß die Entropie S von der Zeit abhängt. Präziser ausgedrückt, wir betrachten zwei Untersysteme mit den Entropien S und S', die anfangs unter verschiedenen Bedingungen gehalten werden, z.B. auf verschiedenen Temperaturen. Die lokale Produktionsrate der Entropie führt zu einer zeitlichen Entropieänderung (erster Term auf der linken Seite) und einem Entropiefluss (zweiter Term).

Observations of coherent cellular behavior cannot be integrated into widely accepted membrane (pump) theory (MT) and its steady state energetics because of the thermal noise of assumed ordinary cell water and freely soluble cytoplasmic K+. However, Ling disproved MT and proposed an alternative based on coherence, showing that rest (R) and action (A) are two different phases of protoplasm with different energy levels. The R-state is a coherent metastable low-entropy state as water and K+ are bound to unfolded proteins. The A-state is the higher-entropy state because water and K+ are free. The R-to-A phase transition is regarded as a mechanism to release energy for biological work, replacing the classical concept of high-energy bonds. Subsequent inactivation during the endergonic A-to-R phase transition needs an input of metabolic energy to restore the low entropy R-state. Matveev’s native aggregation hypothesis allows to integrate the energetic details of globular proteins into this view.

This paper discusses competing-destinations formulation of the gravity model for the flows of patients from their residential areas to hospitals. This approach explicitly acknowledges the interdependence of the patient flows between a set of alternative hospitals. This competing-destinations based approach may be implemented as a probabilistic demand function or conditional logit model, with a Poisson outcome. A Texas based case study of residential areas and State Mental Hospitals is presented. The results of the estimation lend support to the gravity model. Also, the fact that patient flows have been found to be decreasing in the competition posed by alternative hospitals suggests the superiority of the competing-destinations version of the gravity equation over its classical formulation.

A Universe Model which is based on waveform Time instead of particles.
I applied this view to the Energy (as quanta) and Time in "Special Relativity According to The Waveform Time."(published at academia)

When an object accelerated, the used energy is added to the all quantum of particles. This added energy scattered across all basic energy units until equalizing with each other by interfering vibrations.
When all energy units were equalized, the object becomes in a constant speed.

At the same time, the amplitude of these units is being enlarged.
But also due to length contraction, (on the spatial dimension of motion), the wave length of vibration is narrowing. In fact, this is a result of the relatively change in the Planck Length.

In this situation, while the amplitude increasing, the wavelength is decreasing so the way of vibration is longing.

""""You can see the answers for some questions  in this view by my quora page.""""

This paper examines the impact of gravity on outsourcing. We derive a gravity equation from the classical spatial supply problem in which firms purchase some of their inputs from other firms paying the required transport costs. We also allow for different levels of productivity of the firms and build a gravity equation from entropy maximiza-tion. Even if the gravity equations look similar, we show that their underlying structures are different. In general terms, countries are viewed as competing with each other for interaction. The competing destinations gravity model represents a step forward in the recognition of interdependencies in spatial choice. Thus, we include a variable to explain the spatial structure of outsourcing countries in a geographical system. We find much stronger support for the gravity equation derived from the probabilistic input demand function than for the deterministic gravity model. The model shows that outsourcing is carried out mostly because of factor cost differentials and technological differences, but that distance and the gravity of other countries adversely affect trade in intermediate goods and services.

We investigated the developmental changes in the information parameters of the thymus to define the level of
adaptive resources of this organ. It was revealed that studied parameters undergo cyclic changes in ontogenesis.
Ontogenetic periods characterized by low values of information morphological organization are critical, because at this
time organs are characterized by a low level of regenerative-adaptability and less number of structural elements
constituting a potential reserve.

This paper discusses competing-destinations formulation of the gravity model for the flows of patients from their residential areas to health supplier regions. This approach explicitly acknowledges the interdependence of the patient flows between a set of alternative health supplier regions. This competing-destinations based approach may be implemented as a probabilistic demand function or conditional logit model, with a Poisson outcome. A Texas based case study of residential areas and State Mental Hospitals (SMHs) is presented. The results of the estimation do not lend support to the presence of scale effects in SMHs due to the size of population. This result, combined with the negative effect of ALOS and with the positive effect of the provision of forensic services on patient flows, highlights the problem of caseload growth in SMHs.

We invoke the arguments of Qian JJ (1996) Phys A: Math Gen 29: 1305-1309 and show that the application of Maximum Entropy (MaxEnt) approach to a 2D incompressible flow behind a circular cylinder with Reynolds number = 100 is not invariant with respect to scaling transformations, like those involved when changing the system of units from SI to CGS.

This paper examines the impact of gravity on outsourcing. We derive a gravity equation from the classical spatial supply problem in which firms purchase some of their inputs from other firms paying the required transport costs. We also allow for different levels of productivity of the firms and build a gravity equation from entropy maximiza-tion. Even if the gravity equations look similar, we show that their underlying structures are different. In general terms, countries are viewed as competing with each other for interaction. The competing destinations gravity model represents a step forward in the recognition of interdependencies in spatial choice. Thus, we include a variable to explain the spatial structure of outsourcing countries in a geographical system. We find much stronger support for the gravity equation derived from the probabilistic input demand function than for the deterministic gravity model. The model shows that outsourcing is carried out mostly because of factor co...

We attempt a connection between thermodynamics and zatrikean pregeometry, i.e., a chess-like pregeometry. In zatrikean pregeometry space is represented by the abacus, a discrete chessboard-like structure consisting of a sufficiently large number of plaquettes called geobits. The particles move on the abacus from one geobit to the next following certain rules that resemble the game of chess. The sets of rules imposed on the motions of particles on the abacus are called premetrics. There is a variety of paths (called subabaces) leading from one geobit to another, and there is a class consisting of subabaces with the minimum number of geobits. These are called alyssoids (respectively, class of alyssoids) for the particular premetric, while those alyssoids with minimum length are called geodesics (respectively, class of geodesics) for the particular premetric. The so-called zatrikean geodesic was originally defined in G93 (Section 2) as the geodesic most closely following the line segment joining the two geobits. It is also called algorithmic geodesic since it is drawn with the assistance of four simple algorithms. This is a rectifiable curve; and a connection between rectifiable curves and thermodynamics is already available (DuPain, Kamae and Mendes-France 1986). Consequently, the so-called thermodynamic geodesic is defined as the particular member of the class of geodesics with maximum entropy. Since it does not necessarily correspond to the algorithmic geodesic, a new algorithm is devised that draws the geodesic with maximum entropy. Furthermore, the probability of each member of the class of geodesics can be determined as the difference of its entropy from the entropy of the thermodynamic geodesic.

We have studied the quantum entropy
for systems which are coupled to sinks or sources.
We generalize the von Neumann entropy to this case
and prove that its production is in general different from zero.
Such a generalization captures the expected behavior of the entropy
as a measure of disorder in quantum dissipative systems.
We illustrate the theory by explicitly
studying a tunneling model with two energy levels and detuning.

I possess a wide range of experience critiquing and editing academic literature including abstracts, articles, book chapters, proposals and thesis drafts. I have edited ESL work from international scholars and international PhD students from Brazil to Romania to Germany. I am currently Co-editing a Festschrift project from proposal to final manuscript, incorporating input from authors, consultants and reviewers. My editing services include copy editing, content editing, style editing and proof reading. Topics of expertise include, but are not limited to, Humanities Computing, Philosophy, History, Religion, Digital Humanities, Information Ethics, Philosophy of Information, Digital Citizenship, Global Citizenship, and Intercultural Information Ethics. Services available at www.jaredbielby.com

The aim of the present dissertation is to analyze the meaning of the entropy bounds of the holographic sector once tested for statistical ensembles of particles, in order to deeper investigate the nature of these constraints and their mutual links. From the Universal Ener-
gy Bound (UEB) simple time constraints can be argued, which are manifestations of the discrete nature of the space-time and of the presence of ultimate space-time scales. From the combined effort of the UEB and of the Holographic bound by `t Hooft and Susskind, an
entropy density bound as a function of temperature is achieved.

We invoke the arguments of Qian JJ (1996) Phys A: Math Gen 29: 1305-1309 and show that the application of Maximum Entropy (MaxEnt) approach to a 2D incompressible flow behind a circular cylinder with Reynolds number = 100 is not invariant with respect to scaling transformations, like those involved when changing the system of units from SI to CGS.