Relevant bibliographies by topics / Definitions of entropy

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Academic literature on the topic 'Definitions of entropy'

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Published: 24 April 2022

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Journal articles on the topic "Definitions of entropy"

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Yu, Bicheng, Xuejun Zhao, Mingfa Zheng, Xiujiu Yuan, and Bei Hou. "Entropy on Intuitionistic Fuzzy Sets and Hesitant Fuzzy Sets." Journal of Mathematics 2022 (February 7, 2022): 1–10. http://dx.doi.org/10.1155/2022/1585079.

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Since the sufficient conditions for the maximum value of the intuitionistic fuzzy entropy are not unified and the hesitant fuzzy entropy cannot be compared when the lengths of the hesitation fuzzy elements are not equal, improved axiomatic definitions of intuitionistic fuzzy entropy and hesitant fuzzy entropy are proposed, and new intuitionistic fuzzy entropy and hesitant fuzzy entropy based on the improved axiomatic definitions are established. This paper defines the fuzzy entropy that satisfies the properties based on the axiomatized definition of fuzzy entropy and, based on the fuzzy entropy, defines new intuitionistic fuzzy entropy and hesitant fuzzy entropy, so that the three are unified in form. The validity and rationality of the proposed intuitionistic fuzzy entropy and hesitant fuzzy entropy are verified by analysis.
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Anderson, Neal G. "Irreversible information loss: Fundamental notions and entropy costs." International Journal of Modern Physics: Conference Series 33 (January 2014): 1460354. http://dx.doi.org/10.1142/s2010194514603548.

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Landauer's Principle (LP) associates an entropy increase with the irreversible loss of information from a physical system. Clear statement, unambiguous interpretation, and proper application of LP requires precise, mutually consistent, and sufficiently general definitions for a set of interlocking fundamental notions and quantities (entropy, information, irreversibility, erasure). In this work, we critically assess some common definitions and quantities used or implied in statements of LP, and reconsider their definition within an alternative “referential” approach to physical information theory that embodies an overtly relational conception of physical information. We prove an inequality on the entropic cost of irreversible information loss within this context, as well as “referential analogs” of LP and its more general restatement by Bennett. Advantages of the referential approach for establishing fundamental limits on the physical costs of irreversible information loss in communication and computing systems are discussed throughout.
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Jia, Lifen. "A New Definition of Cross-Entropy for Uncertain Sets." Journal of Uncertain Systems 14, no. 02 (2021): 2150013. http://dx.doi.org/10.1142/s1752890921500136.

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Cross-entropy for uncertain sets is used to measure the divergence between two membership functions. Sine cross-entropy, logarithm cross-entropy and quadratic cross-entropy for uncertain sets have been proposed, all the definitions fail to measure the degree of divergence associated with some uncertain sets. Thus, this paper presents a new definition of cross-entropy for uncertain sets as a supplement, and investigates its properties. In addition, this paper also proposes a definition of generalized cross-entropy for uncertain sets, and discusses its properties.
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Teixeira, Andreia, André Souto, and Luís Antunes. "On Conditional Tsallis Entropy." Entropy 23, no. 11 (2021): 1427. http://dx.doi.org/10.3390/e23111427.

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There is no generally accepted definition for conditional Tsallis entropy. The standard definition of (unconditional) Tsallis entropy depends on a parameter α that converges to the Shannon entropy as α approaches 1. In this paper, we describe three proposed definitions of conditional Tsallis entropy suggested in the literature—their properties are studied and their values, as a function of α, are compared. We also consider another natural proposal for conditional Tsallis entropy and compare it with the existing ones. Lastly, we present an online tool to compute the four conditional Tsallis entropies, given the probability distributions and the value of the parameter α.
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Qing, Ming. "The Unique Representations of Fuzzy Entropy for a Finite Fuzzy Set." Applied Mechanics and Materials 433-435 (October 2013): 766–69. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.766.

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Many methods were presented to define fuzzy entropy to measure fuzzy degree of a fuzzy set and a variety of fuzzy entropy formulae were derived and constructed from the definitions of fuzzy entropy. In this paper, a new definition of fuzzy entropy is presented based on a simple order relation and computation formulae of fuzzy entropy is given. Then, the unique representations of fuzzy entropy are given by applying several set of reasonable conditions to fuzzy entropy.
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Gao, Ming Mei, Tao Sun, Rui Ping Xu, Li Song, and Hui Qun Zhang. "An Improved Axiomatic Definition and Structural Formula of Interval-Valued Intuitionistic Fuzzy Entropy." Applied Mechanics and Materials 644-650 (September 2014): 1556–59. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.1556.

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In view of the defects of existing axiomatic definitions of interval-valued intuitionistic fuzzy entropy, an improved axiomatic definition of the interval-valued intuitionistic fuzzy entropy is presented and the corresponding formula is structured in the paper. Firstly, defects in three kinds of the axiomatic system of entropy of IVIFS are analyzed in detail respectively. New axiomatic entropy definition is proposed for the sake of more reasonable depiction of the fuzziness of IVIFS. Based on the new axiomatic entropy definition, a new computational formula is mentioned. Finally, an example is showed to illustrate the effectiveness of this new formula. Overall, the results indicate that the improved axiomatic definition and the new proposed formula are reasonable and effective.
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Livadiotis, George, and David J. McComas. "Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect." Entropy 23, no. 12 (2021): 1683. http://dx.doi.org/10.3390/e23121683.

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This paper develops explicit and consistent definitions of the independent thermodynamic properties of temperature and the kappa index within the framework of nonextensive statistical mechanics and shows their connection with the formalism of kappa distributions. By defining the “entropy defect” in the composition of a system, we show how the nonextensive entropy of systems with correlations differs from the sum of the entropies of their constituents of these systems. A system is composed extensively when its elementary subsystems are independent, interacting with no correlations; this leads to an extensive system entropy, which is simply the sum of the subsystem entropies. In contrast, a system is composed nonextensively when its elementary subsystems are connected through long-range interactions that produce correlations. This leads to an entropy defect that quantifies the missing entropy, analogous to the mass defect that quantifies the mass (energy) associated with assembling subatomic particles. We develop thermodynamic definitions of kappa and temperature that connect with the corresponding kinetic definitions originated from kappa distributions. Finally, we show that the entropy of a system, composed by a number of subsystems with correlations, is determined using both discrete and continuous descriptions, and find: (i) the resulted entropic form expressed in terms of thermodynamic parameters; (ii) an optimal relationship between kappa and temperature; and (iii) the correlation coefficient to be inversely proportional to the temperature logarithm.
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Stoyanov, Luchezar. "Topological and metric entropy for group and semigroup actions." Topological Algebra and its Applications 7, no. 1 (2019): 38–47. http://dx.doi.org/10.1515/taa-2019-0004.

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AbstractIt is well-known that the classical definition of topological entropy for group and semigroup actions is frequently zero in some rather interesting situations, e.g. smooth actions of ℤk+ (k >1) on manifolds. Different definitions have been considered by several authors. In the present article we describe the one proposed in 1995 by K.H.Hofmann and the author which produces topological entropy not trivially zero for such smooth actions. We discuss this particular approach, and also some of the main properties of the topological entropy defined in this way, its advantages and disadvantages compared with the classical definition. We also discuss some recent results, obtained jointly with Andrzej Biś, Dikran Dikranjan and Anna Giordano Bruno, of a similar definition of metric entropy, i.e. entropy with respect to an invariant measure for a group or a semigroup action, and some of its properties.
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Ben-Naim, Arieh. "Entropy and Time." Entropy 22, no. 4 (2020): 430. http://dx.doi.org/10.3390/e22040430.

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The idea that entropy is associated with the “arrow of time” has its roots in Clausius’s statement on the Second Law: “Entropy of the Universe always increases.” However, the explicit association of the entropy with time’s arrow arises from Eddington. In this article, we start with a brief review of the idea that the “increase in entropy” is somehow associated with the direction in which time increases. Then, we examine three different, but equivalent definitions of entropy. We find that none of these definitions indicate any hint of a relationship between entropy and time. We can, therefore, conclude that entropy is a timeless quantity. We also discuss the reasons as to why some scientists went astray in associating entropy with time’s arrow. Finally, we shall discuss Boltzmann’s H-Theorem, which is viewed by many as a proof of the Second Law of Thermodynamics.
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Matty, Michael, Lachlan Lancaster, William Griffin, and Robert H. Swendsen. "Comparison of canonical and microcanonical definitions of entropy." Physica A: Statistical Mechanics and its Applications 467 (February 2017): 474–89. http://dx.doi.org/10.1016/j.physa.2016.10.030.

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Dissertations / Theses on the topic "Definitions of entropy"

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Xin, Ying. "Complex Dynamical Systems: Definitions of Entropy, Proliferation of Epithelia and Spread of Infections and Information." Ohio University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1522955730251256.

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Yi, Ju Y. "Definition and Construction of Entropy Satisfying Multiresolution Analysis (MRA)." DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/5057.

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This paper considers some numerical schemes for the approximate solution of conservation laws and various wavelet methods are reviewed. This is followed by the construction of wavelet spaces based on a polynomial framework for the approximate solution of conservation laws. Construction of a representation of the approximate solution in terms of an entropy satisfying Multiresolution Analysis (MRA) is defined. Finally, a proof of convergence of the approximate solution of conservation laws using the characterization provided by the basis functions in the MRA will be given.
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Hooper, Jack Charles. "Vertical landing flight envelope definition." Thesis, Luleå tekniska universitet, Rymdteknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-80717.

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This paper will investigate the development of a landing footprint for a re-entry vehicle. Vehicles can re-enter the atmosphere with a range of orientations, velocities and flight path angles. The central question is whether a vehicle with any combination of these states can be brought to an acceptable landing condition at a particular landing site and with a particular landing speed. To aide in this investigation several models must be implemented, including that of the atmosphere, the vehicles, the Earth, and the aerodynamics. A detailed analysis of the aerodynamic model will be treated, and the equations of motion subject to these aerodynamic laws will then be compared to results from existing atmospheric reentry software. The principles of optimization will then be employed to generate the footprint of landable states, based on maximum and minimum possible downrange distances, for two vehicle concepts.
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Thiele, Cristiano. "Desenvolvimento da arquitetura dos codificadores de entropia adaptativos CAVLC e CABAC do padrão H.264/AVC." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2012. http://hdl.handle.net/10183/85463.

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Um codificador de entropia é responsável pela representação simbólica de dados de forma a representá-los com um menor número de bits. O H.264/AVC possui três codificadores de entropia: o Exponencial Golomb, o CAVLC que é o codificador de menor complexidade porém com um throughput maior de dados e o CABAC, com maior complexidade e com uma maior capacidade de compressão. A complexidade do codificador de entropia e a dependência dos dados sequenciais no bitstream original são os principais desafios para atender os requisitos de desempenho para compressão em tempo real. Por isso o desenvolvimento destas arquiteturas em hardware dedicado se faz necessário. Neste contexto, esta dissertação descreve os algoritmos que fazem parte da entropia do padrão H.264/AVC e as arquiteturas para estes codificadores entrópicos (Exponential Golomb, CAVLC e CABAC), além de uma arquitetura de hardware dedicada que integra todos estes a um montador final que atende às especificações da norma H.264/AVC. As arquiteturas foram escritas em VHDL e sintetizadas para dispositivos integrados FPGA. Em um dispositivo Virtex-5, este codificador de entropia completo suporta codificação de vídeos no nível 4.2 do padrão H.264/AVC (Full HD a 60 quadros por segundo). Esta arquitetura é a que apresenta o melhor desempenho de processamento dentre os melhores trabalhos relacionados, além de ser um codificador com todas as alternativas de codificação de entropia requeridas pela norma implementadas em um mesmo módulo.<br>An entropy encoder is responsible for the symbolic representation of a data stream so that the final representation contains less bits than the original. The H.264/AVC has three entropy coding schemes: the Exponential Golomb, the CAVLC encoder, that is less complex but with a higher data throughput, and the CABAC that is more complex while allowing for higher compression capability. The complexity of the entropy encoding and data dependencies on the original bitstream are the main challenges to meet the performance requirements for real-time compression. The development of these architectures in dedicated hardware is therefore necessary for high performance encoders. In this context, this work describes the algorithms that are part of the entropy encoders of the H.264/AVC standard, and the corresponding entropy coding architectures (Exponential Golomb, CAVLC and CABAC), plus a dedicated hardware architecture that integrates all of these encoders to a final bitstream assembler that is compliant to the aforementioned standard. The architectures were written in VHDL and synthesized into FPGA devices. In a Virtex-5 device, this full entropy encoder supports video encoding at level 4.2 of the H.264/AVC standard (Full HD at 60 frames per second). The developed architecture performs best among the most recent related architectures published, and has the unique feature of an encoder that implements in the same module all the alternative entropy encoders present in this standard for video compression.
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Komarasamy, Mageshwari. "Deformation Micro-mechanisms of Simple and Complex Concentrated FCC Alloys." Thesis, University of North Texas, 2015. https://digital.library.unt.edu/ark:/67531/metadc822829/.

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The principal objective of this work was to elucidate the effect of microstructural features on the intrinsic dislocation mechanisms in two FCC alloys. First alloy Al0.1CoCrFeNi was from a new class of material known as complex concentrated alloys, particularly high entropy alloys (HEA). The second was a conventional Al-Mg-Sc alloy in ultrafine-grained (UFG) condition. In the case of HEA, the lattice possess significant lattice strain due to the atomic size variation and cohesive energy differences. Moreover, both the lattice friction stress and the Peierls barrier height are significantly larger than the conventional FCC metals and alloys. The experimental evidences, so far, provide a distinctive identity to the nature and motion of dislocations in FCC HEA as compared to the conventional FCC metals and alloys. Hence, the thermally activated dislocation mechanisms and kinetics in HEA has been studied in detail. To achieve the aim of examining the dislocation kinetics, transient tests, both strain rate jump tests and stress relaxation tests, were conducted. Anomalous behavior in dislocation kinetics was observed. Surprisingly, a large rate sensitivity of the flow stress and low activation volume of dislocations were observed, which are unparalleled as compared to conventional CG FCC metals and alloys. The observed trend has been explained in terms of the lattice distortion and dislocation energy framework. As opposed to the constant dislocation line energy and Peierls potential energy (amplitude, ΔE) in conventional metals and alloys, both line energy and Peierls potential undergo continuous variation in the case of HEA. These energy fluctuations have greatly affected the dislocation mobility and can be distinctly noted from the activation volume of dislocations. The proposed hypothesis was tested by varying the grain size and also the test temperature. Activation volume of dislocations was a strong function of temperature and increased with temperature. And the reduction in grain size did not affect the dislocation mechanisms and kinetics. This further bolstered the hypothesis. The second part deals with deformation characteristics of Al-Mg-Sc alloy. The microstructure obtained from the severe plastic deformation (SPD) techniques differ in dislocation density, grain/cell size, and in the grain boundary character distribution. Therefore, it is vital to understand the deformation behavior of the UFG materials produced by various SPD techniques, as the microstructural features basically control the deformation mechanisms. In this study, a detailed analysis was made to understand the deformation mechanisms operative in various regimes of a stress-strain in UFG Al-Mg-Sc alloy produced via friction stir processing. The stress-strain curves exhibited serrations from the onset of yielding to the point of sample failure. The serration amplitude and frequency was higher in UFG material as compared to CG material. Furthermore, the microstructural features that result in the serrated flow were investigated along with the avalanche characteristics. The presence of both ultrafine grains and Al3Sc precipitates were the necessary conditions to reach the critical stress required to push the grain boundary into a critical state to set off an avalanche. The microstructural conditions that did not satisfy both the requirements did not exhibit deep serrations.
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Pennerstorfer, Astrid, and Dieter Pennerstorfer. "How small are small markets? Local market size for child care Services, Working Paper No. 1814." Department of Economics, Johannes Kepler University of Linz, 2019. http://epub.wu.ac.at/7022/1/wp1814.pdf.

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In this article, we propose an innovative way of delineating local markets based on easily accessible data. We apply this concept to the day care industry and investigate providers' location choices relative to local market characteristics to evaluate the widespread presumption that local markets for child care services are geographically very small. Using a panel of all day care centers for the metropolitan region of Vienna, Austria, for nearly a decade, as well as geographically extremely disaggregated data on the spatial distribution of children under the age of six at the 250m×250m grid cell level, we find that the location of children and day care centers are strongly related, but this relationship diminishes as soon as the distance between a child's place of residence and the day care center's location increases. We conclude that local markets for day care services in metropolitan regions are indeed very small (about 500m or 550 yards).
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Mabrak, Sami. "La macrostructure et la microstructure des dictionnaires historiques : etude analytique et comparative de la macrostructure et de la microstructure des dictionnaires historiques français, anglais et arabe." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE2089.

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Notre thèse relève du domaine de la lexicographie et plus précisément de la lexicographie contemporaine. Notre étude analyse les dictionnaires historiques comme objet de recherche. Quant à notre problématique de recherche, elle porte sur la constitution de la macrostructure et sur l’élaboration de la microstructure des dictionnaires historiques que sont le Dictionnaire Historique de la Langue Française (le RH), le Dictionnaire Historique de la Langue Anglaise (l’OED) et le Dictionnaire Historique de la Langue Arabe (le DHLA). Les deux premiers dictionnaires historiques sont déjà publiés, alors que le dernier est en cours de compilation.Notre étude comporte deux objectifs principaux. Tout d’abord, elle analyse les éléments de divergence et les éléments de convergence entre la macrostructure et la microstructure des deux dictionnaires historiques, que sont le RH et l’OED. Ensuite, elle examine ces éléments et détermine ceux qui sont applicables dans la constitution de la macrostructure et l’élaboration de la microstructure du DHLA. Pour ce faire, nous avons opté pour l’analyse d’un corpus issu principalement des dictionnaires - le RH et l’OED. Nous avons fait appel également à un corpus secondaire constitué à partir des dictionnaires français, anglais et arabe de langue générale.Notre étude a permis de confirmer que les trois dictionnaires historiques adoptent trois approches différentes dans la constitution de leur macrostructure. Le RH adopte une approche étymologique. Quant à l’OED, il utilise une approche lexicale. Enfin, le DHLA a opté pour une approche complexe. En revanche, ces trois approches sont mises en œuvre en appliquant trois critères, à savoir, tout d‘abord un critère diachronique, puis un critère orthographique et enfin un critère étymologique. En outre, notre étude a permis de confirmer également que la mise en ordre des entrées principales impacte directement la mise en ordre des entrées secondaires.Quant à la microstructure, les trois dictionnaires élaborent la définition de leurs entrées en adoptant relativement le même modèle. En dernière instance, il s’agit d’un modèle construit à partir de trois types d’informations : des informations d’ordre morphologique, des informations d’ordre sémantique et enfin des informations contextuelles<br>Our thesis is part of the field of lexicography and more precisely of contemporary lexicography. Our study analyses historical dictionaries as a research object. As for the subject of the thesis, it concerns the constitution of the macrostructure and the development of the microstructure for historical dictionaries, which are: the French Historical Dictionary (RH), the English Historical Dictionary (OED) and the Arabic Historical Dictionary (DHLA). The first two are alread published while the third is in progress.Our study has two main goals. First of all it analyses the divergent and convergent elements between macrostructure and microstructure of both RH and OED historical dictionaries. Then it examines these elements and determines those which are applicable in the constitution of macrostructure and the development of DHLA microstructure. To do this, we have chosen the analysis of a corpus mainly from RH and OED dictionaries. We have also appealed to a secondary corpus constituted from general language dictionaries.Our study has affirmed that the three historical dictionaries adopt three different approaches to constitute their macrostructure: etymological for the RH and lexical for the OED, while the DHLA has opted for a complex approach. However these three approaches are implemented by applying three criteria namely, diachronic criterion, orthographical criterion, and etymological criterion. Our study also confirmed that putting main entrances in order directly impacts on the secondary entrances order.As for the microstructure, the three dictionaries elaborate the definition of their entrances by adopting a relatively similar model, built upon three types of information: morphological information, semantic information and contextual information
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Lee, Vaughan Hubert. "A new HD video compression scheme using colourisation and entropy." Thesis, 2012. http://hdl.handle.net/10210/7882.

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M.Ing.<br>There is a growing demand for HD video content. That demand requires significant bandwidth, even with sophisticated compression schemes. As the demand increases in popularity, the bandwidth requirement will become burdensome on networks. In an effort to satisfy the demand for HD, improved compression schemes need to be investigated together with increasing efficiency of transmission. The purpose of this literature study is to investigate existing video compression schemes and techniques used in software implementations. Then to build on existing work within the mature field of video compression, in order to propose a new scheme which would then be tested for viability. Two algorithms were proposed as a result of the literature study. The first algorithm is an improved way to add colour to luminance images of similar scene content. The second algorithm is an encoding scheme that is adaptive to the video content. The proposed encoding scheme adaptively selects to encode the next several frames using well established techniques or to use a technique proposed in this work. At the time of preparing this document, and from the available literature this second proposed algorithm is new. An interesting compression tool has been developed during this study. This tool can be used to obtain a visual expectation of the achievable compression before applying the compression. The tool is a quadrant plot of the difference in image entropy between successive frames and an estimation of the mean percentage motion content between these frames. Over the duration of a scene, the spread of results reveals the extent of the potential compression gain.
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Brink, Anton David. "Image models and the definition of image entropy applied to the problem of unsupervised segmentation." Thesis, 2016. http://hdl.handle.net/10539/20956.

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A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, March 1994.<br>Region segmentation of digital imges by unsupervised thresholding is a common, conceptually simple and important branch of image processing and analysis. Its applications range from that of simple binarization to serving as a useful pre-processing stage for operations such as pattern recognition and image restoration. While many different algorithms have been proposed for the automatic selection of the "correct" threshold the results vary widely in their general usefulness. A class of selection schemes is based on the principle of maximum entropy. This formalism, While effective, is usually involed without reference to its origins or its relationship to images. This thesis attempts to clarify the definition of what is meant by the entropy of an image, to which end various image and Image segmentation models are discussed and proposed. Some apparent shortcomings related to the use of the Shannon entropy formula are addressed and the outcome of the research is applied to the problem of threshold selection. The results indicate a marked improvement in performance of methods using some form(s) of context-related information over those which simply apply the entropy formula without regard to its spatially insensitive nature. Evaluation of results and processes is usually based
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Leon, Lucia, and 梁莉霞. "Definition of a Decision Making Process for Market Entry Strategy Under a Transaction Cost Analysis and a Resource-Based View." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/55428719663417374929.

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碩士<br>國立交通大學<br>企業管理碩士學程<br>99<br>A firm’s choice of the mode of entry into a foreign market is one of the most important decisions made by multinational companies. The entry mode chosen affects how much control the firm enjoys over its business activities and the degree to which it succeeds in foreign markets. Inappropriate entry mode decisions are difficult to change when long-term contracts and large resource commitments are made. The following research analyzes the entry modes of Taiwanese companies related to the Information Electronics Industry. The study is conducted under a theoretical model that unifies concepts from Theory of the Firm and Business Management in order to provide a decision flow that helps evaluate the best way to invest in a foreign market, depending on the nature of the knowledge the firm possess and the characteristics of the local host market. It was determined that due to the characteristics of the knowledge that is possessed on the Information Electronic Industry, it is more appropriate for a company to enter a market with a Greenfield Investment in order to protect its know-how and enjoy high rent generation of this competence for the long term.
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Books on the topic "Definitions of entropy"

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Tenney, James. META Meta ⌿ Hodos. Edited by Larry Polansky, Lauren Pratt, Robert Wannamaker, and Michael Winter. University of Illinois Press, 2017. http://dx.doi.org/10.5406/illinois/9780252038723.003.0007.

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James Tenney introduces a number of propositions, along with corresponding definitions and comments, concerning perceptual organization, musical parameters, formal perception and description, and entropy as a measure of variation. Among these propositions are: temporal gestalt-units (TGs) are formed at several different hierarchical levels during the process of musical perception; the perceptual formation of TGs at any hierarchical level is determined by a number of factors of cohesion and segregation, the most important of which are proximity and similarity; pitch, timbre, and (musical) time are not simply one-dimensional parameters, because each includes at least two relatively independent “subparameters”; the perception of form at any hierarchical level involves the apprehension of three distinct aspects of form at that and all lower levels—state, shape, and structure; the statistical entropy of an ergodic TG is zero.
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Sherwood, Dennis, and Paul Dalby. Free energy. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782957.003.0013.

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A critical chapter, explaining how the principles of thermodynamics can be applied to real systems. The central concept is the Gibbs free energy, which is explored in depth, with many examples. Specific topics addressed are: Spontaneous changes in closed systems. Definitions and mathematical properties of Gibbs free energy and Helmholtz free energy. Enthalpy- and entropy-driven reactions. Maximum available work. Coupled reactions, and how to make non-spontaneous changes happen, with examples such as tidying a room, life, and global warming. Standard Gibbs free energies. Mixtures, partial molar quantities and the chemical potential.
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Chad, Gaffield, Baskerville Peter, and Vancouver Island Project, eds. Field definitions and data entry guide for archival material: A working document. Vancouver Island Project, 1985.

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Sherwood, Dennis, and Paul Dalby. The Second Law of Thermodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782957.003.0009.

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The Second Law. The definition of entropy, and its mathematical properties. The Clausius inequality, and the criterion of spontaneity of change in an isolated system. Worked examples of heat flow down a temperature gradient, and the adiabatic expansion of a gas into a vacuum. Combining the First and Second Laws, with worked examples, such as phase changes. Introduction to the Third Law of Thermodynamics. Introduction to T,S diagrams.
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Stuart, Casey-Maslen, Clapham Andrew, Giacca Gilles, and Parker Sarah. Art.22 Entry into Force. Oxford University Press, 2016. http://dx.doi.org/10.1093/law/9780198723523.003.0026.

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This chapter examines the ATT’s entry into force which is covered by Article 22 of the ATT. The treaty entered into force on 24 December 2014 in accordance with Article 22(1). For states that ratified the treaty after this date, they become party ninety days after the date of deposit of their instrument of ratification, acceptance, approval, or accession with the treaty Depositary, the UN Secretary-General. Article 22 is linked to the treaty as a whole insofar as it determined both when the ATT entered into force and when each state adhering to the treaty becomes party to it. According to Article 5(3), the definitions of arms and items under the treaty depended on the date of entry into force.
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Sherwood, Dennis, and Paul Dalby. Reactions in solution. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782957.003.0016.

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Another key chapter, examining reactions in solution. Starting with the definition of an ideal solution, and then introducing Raoult’s law and Henry’s law, this chapter then draws on the results of Chapter 14 (gas phase equilibria) to derive the corresponding results for equilibria in an ideal solution. A unique feature of this chapter is the analysis of coupled reactions, once again using first principles to show how the coupling of an endergonic reaction to a suitable exergonic reaction results in an equilibrium mixture in which the products of the endergonic reaction are present in much higher quantity. This demonstrates how coupled reactions can cause entropy-reducing events to take place without breaking the Second Law, so setting the scene for the future chapters on applications of thermodynamics to the life sciences, especially chapter 24 on bioenergetics.
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Basu, Anuradha. Ethnic Minority Entrepreneurship. Edited by Anuradha Basu, Mark Casson, Nigel Wadeson, and Bernard Yeung. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780199546992.003.0021.

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This article reviews the existing theoretical and empirical literature on ethnic entrepreneurship. It primarily focuses on empirical research conducted in Britain and the United States. It examines the definition of ethnic entrepreneurship and evaluates the forces affecting entry into ethnic entrepreneurship, entrepreneurial survival and success, as well as the factors underlying the heterogeneity in entrepreneurial behaviour and performance among ethnic minority groups.
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Jones, Alison, and Brenda Sufrin. 1. Introduction to Competition Law. Oxford University Press, 2016. http://dx.doi.org/10.1093/law/9780198723424.003.0001.

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All books in this flagship series contain carefully selected substantial extracts from key cases, legislation, and academic debate, providing able students with a stand-alone resource. This introductory chapter discusses the following: the objectives of competition law; US law; schools of competition analysis and theories and concepts relevant to competition law; ordoliberalism and its implications for competition policy; EU competition law; competition law and the international context; the techniques and tools of competition law; and market power, market definition, and barriers to entry.
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Jeswald W, Salacuse. 5 The General Structure of Investment Treaties. Oxford University Press, 2015. http://dx.doi.org/10.1093/law/9780198703976.003.0005.

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This chapter discusses the basic structure of most modern investment treaties, which encompasses ten topics: treaty title and statement of purpose; definitions and scope of application; conditions for the entry of foreign investment and investors; general standards of treatment of foreign investments and investors; monetary transfers; expropriation and dispossession; operational and other conditions; losses from armed conflict or internal disorder; treaty exceptions, modifications, and terminations; and dispute settlement. Despite divergence among individual treaties, as a group they demonstrate many commonalities, including their coverage of similar issues and their use of equivalent or comparable legal concepts and vocabulary. It is these commonalities, despite individual differences, that are contributing to the creation of a global regime for international investment.
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Black, John, Nigar Hashimzade, and Gareth Myles. A Dictionary of Economics. Oxford University Press, 2017. http://dx.doi.org/10.1093/acref/9780198759430.001.0001.

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Over 3,500 entriesThis authoritative and comprehensive dictionary contains clear, concise definitions of key economic terms. Covering all aspects of economics including economic theory and policy, applied microeconomics and macroeconomics, labour economics, public economics and public finance, monetary economics, and environmental economics, this is the essential reference work in this area.Entries are supplemented by entry-level web links, and useful appendices include a list of institutional acronyms and their affiliated websites, a list of Nobel prize-winners in economics, the Greek alphabet, and a list of relevant websites.This dictionary is an essential guide for students and teachers of economics, business, and finance, as well as for professional economists and anyone who has to deal with economic data.
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Book chapters on the topic "Definitions of entropy"

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Cahill, Nathan D. "Normalized Measures of Mutual Information with General Definitions of Entropy for Multimodal Image Registration." In Biomedical Image Registration. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14366-3_23.

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Dompere, Kofi Kissi. "The Relational Structure Between the General Information Definition and Entropy." In A General Theory of Entropy. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18159-8_1.

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Feuerriegel, Uwe. "Energiebilanzierung, Definitionen, Wärme, Entropie." In Wärmeübertragung mit EXCEL und VBA. Springer Fachmedien Wiesbaden, 2021. http://dx.doi.org/10.1007/978-3-658-35906-5_4.

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Belavkin, Roman V., Panos M. Pardalos, Jose C. Principe, and Ruslan L. Stratonovich. "Definition of information and entropy in the absence of noise." In Theory of Information and its Value. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-22833-0_1.

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Yu, Haitao. "A Novel Fuzzy Entropy Definition and Its Application in Image Enhancement." In Lecture Notes in Electrical Engineering. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-26007-0_2.

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Hoschka, Tobias C. "Cross-Border Penetration of Financial Services in the EC: Definitions and Evolution." In Cross-Border Entry in European Retail Financial Services. Palgrave Macmillan UK, 1993. http://dx.doi.org/10.1007/978-1-349-22979-6_2.

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Poitras Pratt, Yvonne, and Keeta Gladue. "Re-Defining Academic Integrity: Embracing Indigenous Truths." In Academic Integrity in Canada. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-83255-1_5.

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AbstractDespite historical and ongoing challenges, Canada has been making promising strides towards reconciliation prompted in large part by the work of the Truth and Reconciliation Commission of Canada (2015). We honour our Indigenous Elders and Ancestors who have led social and educational movements that named and resisted the negative outcomes created and continued by a Canadian colonial history. The authors point to current institutional projects of decolonizing and Indigenizing the academy as holding the potential to re-define what academic integrity means. As a hopeful point of entry into how teaching and learning scholars might reconsider current conceptions of integrity, we see Indigenizing efforts across a number of Canadian universities as the basis from which to speak to a more inclusive and wholistic definition of academic integrity. The authors seek to problematize the current neoliberal and commercialized approaches to education where different forms of academic misconduct arise as inevitable outcomes. If education is viewed as the pursuit of truth, or more appropriately truths, then it is essential to nuance the scope of academic integrity to include Indigenous perspectives such as wholism and interconnectedness. In this chapter, we discuss these truths, challenging current conceptions, to propose a more inclusive definition of academic integrity by drawing upon Indigenous scholarship as well as dynamic forms of ancestral language to situate our work. In sum, sharing truths through the inclusion of Indigenous perspectives grounds the scholarly discussion in an equitable understanding of truth-telling as foundational to academic integrity.
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Fabbris, Luigi, and Paolo Feltrin. "Measuring the movement between employment and self-employment: a survey proposal." In Proceedings e report. Firenze University Press, 2021. http://dx.doi.org/10.36253/978-88-5518-304-8.14.

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The study concerns the following issues: 1) basic definitions (traditional craftsmanship and commercial work, self-employment, freelance jobs, learned professions, etc.); 2) analysis of the sources on, and the organizations representing the workers of the self-employment compound; 3) medium-to-long term analysis of the main components of the self-employment compound and of the occupation in self-employment companies. We examined various statistical sources on self-employment in Italy, a category including about 5.5 million workers, according to official estimates. We examined the yearly data of the time span from 2009 to 2019, with a concept about 2020, the Covid-19 year. In the examined period, we highlighted a dramatic reduction at employment entry of younger cohorts of less educated people (about one million people), just partly compensated by an increase of new entries of aged and highly educated people. The study concludes with a proposal of a set of questions on self-employment that could be used to adjust the specific part of the questionnaire used by Istat for the survey on the Italian labour forces.
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"Concepts and Definitions." In Energy, Entropy and Engines. John Wiley & Sons, Ltd, 2016. http://dx.doi.org/10.1002/9781119013167.ch2.

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"Qualitative Definitions and Descriptions of Entropy." In The Second Law of Life. Elsevier, 2007. http://dx.doi.org/10.1016/b978-081551537-1.50019-9.

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Conference papers on the topic "Definitions of entropy"

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Sotoudeh, Zahra. "Different Definitions of Entropy for Statistical Energy Analysis." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87240.

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This paper explores several definitions of entropy that stem from the fields of statistical mechanics and thermodynamics for vibrating structures. This paper shows that these definitions are equivalent in the context of mechanically vibrating systems. However, one is more suitable for statistical energy analysis. This work is motivated by the usefulness of the entropy concept towards developing a framework for the statistical treatment of vibroacoustic systems. Specifically, entropy provides a thermodynamic framework to justify the methodology of statistical energy analysis.
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Manis, George, and Roberto Sassi. "A Python Library with Fast Algorithms for Popular Entropy Definitions." In 2021 Computing in Cardiology (CinC). IEEE, 2021. http://dx.doi.org/10.23919/cinc53138.2021.9662811.

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Mahmood, Syed Moez Hussain, Mark G. Turner, and Kiran Siddappaji. "Flow Characteristics of an Optimized Axial Compressor Rotor Using Smooth Design Parameters." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-57028.

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Blade designs have evolved from NACA series and free vortex assumptions to detailed meanline and forced vortex definitions. A design process is presented with numerous parametric options to explore a large design space. Smoothness in turbomachinery blade shapes is critical to an effective design. A cubic B-spline is used to control spanwise variations in the curvature definition of airfoil camber, thickness distribution, leading edge definition, inlet angles and outlet angles as parameters with a small number of control points. Varying parameters of individual blade sections requires more control variables that increases the parameter space and adds kinks in the 3D blade shape. Benefits of this smooth spanwise capability are demonstrated by linking the blade design tool with an aerodynamic optimization system. A single subsonic rotor (rotor 6 of a 10 stage axial compressor derived from the GE EEE design) has been considered as the baseline for the optimization process. Optimization is performed by varying curvature of the airfoil camberline as well as inlet and outlet angles in the spanwise direction. A single objective optimization was performed to optimize isentropic efficiency. An improvement in efficiency of 0.83% from 91.87% to 92.63% was obtained. The optimized blade geometry has a smooth transition from a traditional airfoil shape at the hub section to an S-shaped airfoil at the mid and tip sections. This unique blade shape was obtained because the airfoil camber curvature definition was allowed to vary smoothly spanwise. An S-shaped blade near the mid and tip section promotes flow to move radially downwards which allows for a reduction in entropy generation due to tip leakage flows. Entropy is used to quantify losses and improvement in efficiency.
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Shah, Amip J., and Chandrakant D. Patel. "Designing Environmentally Sustainable Electronic Cooling Systems Using Exergo-Thermo-Volumes." In ASME 2008 2nd International Conference on Energy Sustainability collocated with the Heat Transfer, Fluids Engineering, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/es2008-54089.

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Thermo-volumes allow the design engineer to expediently understand the thermal resistance of a given cooling solution (an indicator of performance) along with its flow resistance (an indicator of the pumping power, or energy consumption, which will be required by the fluid handler). In the present work, we expand upon thermo-volumes by including the lifetime exergy cost (in units of Joules of availability destroyed) as a means to enable the consideration of resource consumption (and thus the environmental sustainability) of the cooling solution. To achieve these exergo-thermo-volumes, we reinterpret previous definitions of thermo-volumes in terms of the entropy generated during heat transfer and fluid flow. The Guoy-Stodola theorem is used to convert this entropy generation into an ‘operational’ exergy loss. Next, based on the material choice and assembly processes used in creating the product, an embedded exergy consumption that accounts for the amount of exergy destroyed during extraction, transportation and disposal of the material is attached to the operational exergy loss. Thus, the total ‘cradle-to-cradle’ exergy loss of the solution is devised. In this framework, the optimal solution will be that which destroys the minimal amount of exergy. Correspondingly, instead of relying upon the COP (which is focused on operational consumption), we propose evaluation of cooling solutions in terms of the heat removal capacity per unit lifetime exergy consumption. The paper concludes by illustrating applicability of the method to the design of an enterprise server. It should be noted that although the paper is focused on electronics cooling solutions, the methodology is designed to be sufficiently general for use in any thermal management application.
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Belavkin, Roman V. "On variational definition of quantum entropy." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING (MAXENT 2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4905979.

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de Zárate, José M. Ortiz. "Definition of frame-invariant Soret coefficients for ternary mixtures." In Entropy 2021: The Scientific Tool of the 21st Century. MDPI, 2021. http://dx.doi.org/10.3390/entropy2021-09879.

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Hough, Elise, and Zahra Sotoudeh. "Statistical Energy Analysis of Vibrating Structures With Energy and Entropy." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-69640.

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Abstract We present a complete thermodynamic analogy of statistical energy analysis (SEA) using entropy and energy for both linear and nonlinear coupled systems. We will use Khinchin’s Entropy as our statistical entropy definition from statistical mechanics. This framework allows for the restrictive assumptions of linearity to be removed from this analysis method. We will use the classical definition of entropy to relate entropy to Vibrational Temperature. Using Khinchin’s statistical definition of entropy for a vibrating system, we will define a Vibrational Temperature as a function of energy. Hence, we will derive all that is necessary to construct the SEA power flow equation along with the transient coupling loss factors without any linearity assumption. With this method one can expand SEA to nonlinear transient coupled systems. We will verify our proposed method using Monte Carlo Simulation and published analytical closed form solutions.
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Vitulano, S., M. Nappi, D. Vitulano, and C. Masuovito. "Edge detection using a new definition of entropy." In Proceedings of 13th International Conference on Pattern Recognition. IEEE, 1996. http://dx.doi.org/10.1109/icpr.1996.546740.

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Gour, Gilad, and Mark M. Wilde. "Entropy of a Quantum Channel: Definition, Properties, and Application." In 2020 IEEE International Symposium on Information Theory (ISIT). IEEE, 2020. http://dx.doi.org/10.1109/isit44484.2020.9174135.

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Rokanujjaman, Md, Md Altab Hossain, Md Rezaul Islam, and Md Shariful Islam. "Effective part definition for gait identification using gait entropy image." In 2013 2nd International Conference on Informatics, Electronics and Vision (ICIEV). IEEE, 2013. http://dx.doi.org/10.1109/iciev.2013.6572551.

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