The information entropy, often just entropy, is a basic quantity in information theory associated. Please recommend a good philosophical book on entropy. What shannon did was to attempt to quantify the amount of information that bob transfers to alice. The principle circumstance that led swenson to the discovery and specification of the law was the recognition by him and others of the failure of the then popular view of. Information theory for intelligent people simon dedeo september 9, 2018 contents 1 twenty questions 1 2 sidebar. Diversityindex entropy is one of several ways to measure diversity. The maximum entropy principle shannon 1948, jaynes 1957 provides a means to obtain leastbiased statistical inference when insufficient information is available stemming from my prior work nem, polygonal fem, the principle of maximum entropy was used to construct basis functi. While in principle all probabilistic quantities associated with a random process. Eminent scholars in various fields of applied information theory have been invited to contribute to this festschrift, collected on the occasion of his 75 th birthday. A theory of abundance, distribution, and energetics. Jan 02, 2016 that depends on what kind of entropy youre interested in. The fundamental idea is that, if the entropy of an information source drops, that means we can ask fewer questions to guess the outcome.
This is the first comprehensive book about maximum entropy principle and its applications to a diversity of fields like statistical mechanics, thermodynamics, business, economics, insurance, finance, contingency tables, characterisation of probability distributions univariate as well as multivariate, discrete as well as continuous, statistical inference, nonlinear spectral analysis of time. The concept of information entropy was introduced by claude shannon in his 1948 paper a mathematical theory of communication. The notion of entropy, which is fundamental to the whole topic of this book. Recall that the table comparison of two encodings from m to s showed that the second encoding scheme would transmit an average of 5. What books introduce entropy in a intuitive, elementary way at most, for a person with undergraduate physics studies. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along. In order to understand shannons entropy, we return to bob and alice and assume that they have a communication channel that is capable of transferring one pulse by seven in the evening. Discover the best physics of entropy in best sellers. On the one hand, the concepts of entropy and information are universal, in the sense that a bit. The maximum entropy method springer series in information. In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. Maximum entropy principle maximum entropy principle arose in statistical mechanics if nothing is known about a distribution except that it belongs to a certain class distribution with the largest entropy should be chosen as the default motivation.
Along the way, well give some intuitive reasoning behind these values in addition to the formulas. Since nonequilibrium evolution of a system is too complex and, as a rule, unstable, its microscopic characteristics may be viewed as random variables. Jul 21, 2015 maximum entropy principle and information math4iqb. Entropy and information theory is highly recommended as essential reading to academics and researchers in the field, especially to engineers interested in the mathematical aspects and mathematicians interested in the engineering applications. We present an application of the principle of maximum entropy to understanding species diversity in ecology and introduce a new statistical ensemble corresponding to the distribution of a variable population of individuals into a set of species not defined a priori. For several decades there exists an ongoing controversy whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. Entropy in information theory has deep ties to the thermodynamic concept of entropy and, as well see, it can be related to the least number of bits it would take on average to communicate x from a one location the sender to another the receiver. Entropy is particularly friendly to such logical shortcuts. Nov 06, 2009 entropy books has issued occasional catalogues and lists over the last 38 years. The entropy of information the distribution of digits benfords law page 141 from the book.
In information theory, entropy is a measure of the uncertainty associated with a random variable. Information theory a tutorial introduction o information theory. This seniorlevel textbook provides a unified conceptual framework for the study of probabilistic systems with its elucidation of three key concepts. About onethird of the book is devoted to shannon source and channel. What is an intuitive explanation of the concept of entropy in. This chapter introduces some of the basic concepts of information theory, as well. Forty years ago, in 1957, the principle of maximum entropy was first intro duced by jaynes into the field of statistical mechanics.
Entropy optimization has become a powerful tool for data analysis and problem solving that has an infinite array of realworld applications. Since that seminal publication, this principle has been adopted in many areas of science and technology beyond its initial application. A history, a theory, a flood by james gleick, the mathematical theory of communication by claude shannon, meta. Shannon, who formulated many of the key ideas of information theory. This might be of philosophical interest, because it may help to clarify the relationship between information and epistemic probability on the one hand, and the laws of nature and physical propensities on the other. The maximum entropy principle also eliminates the mystery as to the origin of the mathematical expressions underlying all probability distributions. Entropy in thermodynamics and information theory from wikipedia, the free encyclopedia there are close parallels between the mathematical expressions for the thermodynamic entropy, usually denoted by s, of a physical system in the statistical thermodynamics established by ludwig boltzmann. The articles cover topics in the areas of physical, biological, engineering and social sciences such as information technology, soft computing, nonlinear systems or molecular biology with a thematic. The law of maximum entropy production lmep or mep was first recognized by american scientist rod swenson in 1988, and articulated by him in its current form below in 1989. Entropy measures, maximum entropy principle and emerging. Introduction the concept of entropy in information theory describes how much information there is in a signal or event. The least action and the maximum entropy principles are the.
Download it once and read it on your kindle device, pc, phones or tablets. Ying nian wu department of statistics, university of michigan, ann arbor, mi 48109, u. So, i searched for books on information theory in places other than reddit, and in my search i found this list of books for anyone else who is also interested in learning information theory. Principle of maximum entropy in chapter 9, we discussed the technique of estimating input probabilities of a process that is consistent with known constraints expressed in terms of averages, or expected values, of one or more quantities, but is otherwise as unbiased as possible. Information on ice 4 3 encoding and memory 4 4 coarsegraining 5 5 alternatives to entropy.
The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge is the one with largest entropy, in the context of precisely stated prior data such as a proposition that expresses testable information. Examples are entropy, mutual information, conditional entropy, conditional information, and. What is the computer science definition of entropy. The term by itself in this context usually refers to the shannon entropy, which quantifies, in the sense of an expected value, the information contained in a message, usually in units such as bits. This is the first comprehensive book about maximum entropy principle and its applications to a diversity of fields like statistical mechanics, thermodynamics, business, economics, insurance, finance, contingency tables, characterisation of probability distributions univariate as well as multivariate, discrete as well as continuous, statistical inference, nonlinear spectral analysis of. That depends on what kind of entropy youre interested in. In the present case, the new approach is to start with information and work from there to entropy, and the new organizing principle is the uni. The maximum entropy principle makes high frequencies. Maximum entropy probability distribution wikipedia. Entropy and information theory universitas lampung.
The book should not necessarily introduce entropy in relation only to thermodynamics, but perhaps more as a standalone physical measurable and in a broader context for example, information entropy. Landauers principle imposes a lower bound on the amount of heat a computer must generate to process. This is the first comprehensive book about maximum entropy principle and its applications to a diversity of fields like statistical mechanics, thermodynamics, business, economics, insurance, finance, contingency tables, characterisation of probability distributions univariate as well as multivariate, discrete as well as continuous, statistical inference, nonlinear spectral analysis of time series, pattern recognition, marketing and elections, operations research and reliability theory. A theory of abundance, distribution, and energetics oxford. A theory of abundance, distribution, and energetics oxford series in ecology and evolution kindle edition by harte, john. The maximum entropy principle is used in statistical physics to find the distribution of these variables in equilibrium. Maximizing entropy minimizes the amount of prior information built into the distribution. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class, then the distribution with the largest entropy should be chosen as the leastinformative default. Entropy information theory news newspapers books scholar jstor february 2019 learn how.
Rather, we should start with an intuitive concept and try to define a mathematical formula satisfying the properties we want it to satisfy in the informal sense. About onethird of the book is devoted to shannon source and channel coding theorems. This book is an updated version of the information theory classic, first published in 1990. Information entropy dynamics and maximum entropy production. Maximum entropy download ebook pdf, epub, tuebl, mobi.
We have shown that the ordinary use of the word information is much different from the word information in information theory. Examples are entropy, mutual information, conditional entropy, conditional information, and relative entropy discrimination, kullbackleibler. Maximum entropy production principle in physics, chemistry. Minimax entropy principle and its application to texture. Use features like bookmarks, note taking and highlighting while reading maximum entropy and ecology.
We have also explained that thermodynamic entropy and the entropy of information theory are the same in terms of increasing randomness. The quantitative measure of the amount of missing information is shannons information entropy. Information entropy is occasionally called shannons entropy in honor of claude e. A guide to entropy and the second law of thermodynamics. Entropy and information theory stanford ee stanford university. The most probable trajectory of the evolution and the information theory. This book is devoted to the theory of probabilistic information measures and. The maximum entropy maxent principle first arose in statistical mechanics, where. Information entropy dynamics and maximum entropy production principle alexander l. Benfords law the relative frequency of a digit in a file of random numbers in not uniform. To do so, the transmitter sends a series possibly just one partial messages that give clues towards the original message. David mumford division of applied mathematics, brown university, providence, ri 02912, u. Another useful relevant principle is the minimum crossentropy principle mcep.
The notion of entropy, which is fundamental to the whole topic of this book, is introduced here. In 1951, this principle was developed by kullback and leibler 26, and it has been one of the most important entropy optimization principles. Complexity, entropy and the physics of information book. The information content of one of these partial messages is a measure of how much uncertainty this resolves for the receiver. Bennaim proposes replacing our understanding of entropy as disorder with entropy as lack of information. Paralleling the derivation of thermodynamics from the maximum entropy principle, the state variable theory of ecology developed in this book predicts realistic forms for all metrics of ecology that describe patterns in the distribution, abundance, and energetics of species over multiple spatial scales, a wide range of habitats, and diverse taxonomic groups. The least action and the maximum entropy principles are the governing dynamics, according to eddington, what do they have in common. Your recommendation appears on that list, so ill be sure to check my local library. Shalymov abstract the asymptotic convergence of probability density function pdf and convergence of differential entropy are examined for the nonstationary processes that follow the maximum entropy principle maxent and maximum. Thanks to shannon, the bit, which is the unit of entropy, is adopted as our quantitative measure of information, or measure of surprise. Entropy books has issued occasional catalogues and lists over the last 38 years. Complexity, entropy and the physics of information by.
We specialize in the wide field of books on books, encompassing typography, graphic design, bibliography, printing, publishing, binding, and papermaking. Jul 21, 2014 i believe a good intuitive explanation enables you to apply a concept without the mental overhead of too many mathematical details. This book is an updated version of the information theory classic, first. Minimax entropy principle and its application to texture modeling song chun zhu division of applied mathematics, brown university, providence, ri 02912, u. Examples are given showing how the maximum entropy principle assigns numerical values to the probabilities in coin tossing, dice rolling, statistical mechanics, and other inferential scenarios. I believe a good intuitive explanation enables you to apply a concept without the mental overhead of too many mathematical details. A primer on shannons entropy and information bourbaphy. Jun 02, 2011 originally published in 1981, this excellent treatment of the mathematical theory of entropy gives an accessible exposition of the ways in which this idea has been applied to information theory, ergodic theory, topological dynamics and statistical mechanics. Entropy and information theory guide books acm digital library. Find the top 100 most popular items in amazon books best sellers. An introduction to information theory and entropy csustan.
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