Binary memory less source has symbols 0 and 1 which have probabilities p0 and p1 1p0. Information theory was not just a product of the work of claude shannon. When this is the case, the units of entropy are bits. By introducing the theory that enabled our information revolution, this book describes what information is, how it can be communicated e ciently. Entropy, thermodynamic entropy, boltzmanns entropy, informationtheory. In the book the authors seek to analyse the worlds economic and social structures by using the second law of thermodynamics, that is, the law of entropy.
In information theory and statistics, negentropy is used as a measure of distance to normality. Entropy and information theory 3 march 20 this site provides the current version of the first edition of the book entropy and information theory by r. The meaning of entropy is different in different fields. That depends on what kind of entropy youre interested in. It tells how much information there is in an event. Entropy, thermodynamic entropy, boltzmanns entropy, information theory. A primer on shannons entropy and information bourbaphy. Entropy information theory synonyms, entropy information theory pronunciation, entropy information theory translation, english dictionary definition of entropy information theory.
Systems science and cybernetics entropy systems theory kenneth d. Aug 10, 2014 in information theory, entropy is a measure of the uncertainty in a random variable. Shannon borrowed the concept of entropy from thermodynamics where it describes the amount of disorder of a system. Using work by faddeev and furuichi, we derive a very simple characterization. Lecture notes on information theory preface \there is a whole book of readymade, long and convincing, lavishly composed telegrams for all occasions. Entropy and information theory first edition, corrected robert m. 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. On a side note, is there any connnection between the entropy that occurs information theory and the entropy calculations in chemistry thermodynamics. On wikipedia, the definition of shannon entropy is the average rate at which information is produced by a stochastic source of data. We can compute or measure the quantity of energy contained in this sheet of paper, and the same is true of its entropy. Find the top 100 most popular items in amazon books best sellers. Entropy simple english wikipedia, the free encyclopedia. Here is an intuitive way of understanding, remembering, andor reconstructing shannons entropy metric for information. Entropy is average information content for the given source symbol.
The concept of entropy in information theory describes how much. How much information a message contains is measured by the extent it combats entropy. Code book with errors code book entropy properties han vinck 20 26. Why is entropy maximised when the probability distribution is. It was an attempt at a discussion of entropy and decay in some literature, mostly via lots of examples, rather than a scientific discussion on how brane collisions could lead to a cyclical universe, whether branes are expected to collide often enough to prevent momentary heat deaths, mond vs. To do so, the transmitter sends a series possibly just one partial messages that give clues towards the original message. Indeed the diversity and directions of their perspectives and interests shaped the direction of information theory. 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. What is entropy and why information gain matter in. Concerning the philosophical aspect, i think each reader has to decide by himself whether the book gives him enough information to answer his personal philosophical questions concerning entropy. The entropy of information the distribution of digits benfords law page 141 from the book. Information theory for intelligent people simon dedeo september 9, 2018 contents 1 twenty questions 1 2 sidebar. The defining expression for entropy in the theory of statistical mechanics established by ludwig boltzmann and j.
By definition, the entropy of a source is given by. Jan 02, 2016 that depends on what kind of entropy youre interested in. Information theory is mathematical, while cognition is a subjective phenomenon. Information theory definition is a theory that deals statistically with information, with the measurement of its content in terms of its distinguishing essential characteristics or by the number of alternatives from which it makes a choice possible, and with the efficiency of processes of communication between humans and machines. Olimpia lombardi 1 federico holik 2 leonardo vanni 3. The concept of information entropy was introduced by claude shannon in his 1948 paper a mathematical theory of communication. This formulation of entropy is closely tied to the allied idea of information. However, for machine learning, we are more interested in the entropy as defined in information theory or shannon entropy. There are numerous characterizations of shannon entropy and tsallis entropy as measures of information obeying certain properties. Therefore i prefer this book to enter into the notion of entropy in its full range. The last few years have witnessed the rapid development of network coding into a research eld of its own in information science. Entropy definition and meaning collins english dictionary.
This chapter introduces some of the basic concepts of information theory, as well. The next two sections will be devoted to argue for the relative. What shannon did was to attempt to quantify the amount of information that bob transfers to alice. For further reading, the following book is recommended. An introduction to information theory and entropy tom carter csu stanislaus. I assumed the oscillators had only 4 energy states and got s1. Entropy is simply a quantitative measure of what the second law of thermodynamics describes. You see, what gets transmitted over the telegraph is not the text of the telegram, but simply the number under which it is listed in the book. Information theory definition of information theory by. Entropy is measured in bits the log is log2 there are two types of entropy.
The information entropy, often just entropy, is a basic quantity in information theory associated. Its impact has been crucial to the success of the voyager missions to deep space. Entropy shows up in a wide variety of contexts including physics, information theory and philosophy. What is the computer science definition of entropy. In this lecture, well cover the basic definitions of entropy, mutual information, and the kullback. The term entropy originated in statistical thermodynamics, which is a subdomain of physics. The amount of information conveyed by each event defined in this way becomes a random variable whose expected value is the information entropy. Reviews of information theory information lies at the heart of biology, societies depend on it, and our ability to process information ever more eciently is transforming our lives. It was the result of crucial contributions made by many distinct individuals, from a variety of backgrounds, who took his ideas and expanded upon them. From information and chaos theory to ghost particles and gravitational waves. Gray information systems laboratory electrical engineering department stanford university springerverlag new york c 1990 by springer verlag. The book provides a unified panoramic view of entropy and the second law of thermodynamics.
Entropy and information theory universitas lampung. Entropy is a state of disorder, confusion, and disorganization. This book is an evolution from my book a first course in information theory published in 2002 when network coding was still at its infancy. Recall that the table comparison of two encodings from m to s showed that the second encoding scheme would transmit an average of 5. Examples are entropy, mutual information, conditional entropy, conditional information, and relative entropy discrimination, kullbackleibler. Sending such a telegram costs only twenty ve cents. 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 devoted to the theory of probabilistic information measures and. Entropy controls how a decision tree decides to split the data. The information content of one of these partial messages is a measure of how much uncertainty this resolves for the receiver. Our galaxy, the solar system, and the biosphere all take their being from entropy, as a result of its transferenceto the surrounding medium.
Elements of information theory fundamentals of computational. Introduction the concept of entropy in information theory describes how much information there is in a signal or event. Nonfiction book by jeremy rifkin and ted howard, with an afterword by nicholas georgescuroegen. Lei maos log book entropy, perplexity and its applications. Entropy is the basic thermodynamic variable that serves to define and relate most thermal properties of matter, and the. I believe a good intuitive explanation enables you to apply a concept without the mental overhead of too many mathematical details. It was originally proposed by claude shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper titled a mathematical theory of communication. In information theory, entropy is a measure of the uncertainty associated with a random variable.
You can see the work of jaynes and many others following his work such as here and here, for instance. Entropy in thermodynamics and information theory wikipedia. Shannon borrowed the idea of entropy from the second law of thermody namics, which states that the universe is winding down from an organized state to chaos, moving from predictability to uncertainty. We also define the conditional entropy of a random variable given another. The notion of entropy, which is fundamental to the whole topic of this book, is. What is an intuitive explanation of the concept of entropy in.
This section provides more resources on the topic if you are looking to go deeper. Entropy is a basic concept in physics and information science, being the basic measure to compare different states of an isolated system the information content of a description. Information processing and thermodynamic entropy stanford. In information theory, a mathematical measure of the degree of randomness in a set of data, with greater randomness implying higher entropy and greater. Lets assume one system could only be in four states, a, b, c, and d of equal probabilities. Information entropy is a concept from information theory.
To illustrate the idea further, both gabor 1964 and brillouin 1951 constructed specific models of dissipative measurement that. Also, information is inherently subjective, because it deals with what you know and what you dont know entropy, as one form of information, is also subjectivethis point makes some physicists uneasy. In the statistical interpretation, entropy s is a measure of uncertainty of a given. Overview shannons metric of entropy of information is a foundational concept of information theory 1, 2. Shannon, who formulated many of the key ideas of information theory. The notion of entropy, which is fundamental to the whole topic of this book, is introduced here. For an overview of the most commonly seen entropies, see what is the easiest definition of entropy. This is intended to be a simple and accessible book on information theory. In general, the more certain or deterministic the event is, the less information it will contain. Entropy is the measures of impurity, disorder or uncertainty in a bunch of examples. Commenges information theory and statistics 3 cross entropy, play a central role in statistics. Information entropy, which is a measure of information communicated by systems that are affected by data noise. Information on ice 4 3 encoding and memory 4 4 coarsegraining 5 5 alternatives to entropy. Generally, entropy refers to disorder or uncertainty, and the definition of entropy used in information theory is directly analogous to the definition used in statistical thermodynamics.
Bailey encyclopedia of life support systems eolss entropy systems theory kenneth d. A characterization of entropy in terms of information loss. Information theory studies the quantification, storage, and communication of information. Entropy and information theory stanford ee stanford university. In section 6, the relation between the definition of information and the coding of information will be discussed. Szilards argument was developed further after shannon identified that the measure p ln p had operational significance for information theory, suggestive of a deeper connection between entropy and information.
Information entropy definition of information entropy by. Discover the best physics of entropy in best sellers. Communication communication involves explicitly the transmission of information from one point to another. So a very simplistic approach to entropy with information theory was only 40% lower than experiment and good theory, for the one set of conditions i tried. In information theory, the major goal is for one person a transmitter to convey some message over a channel to another person the receiver. In his paper \the mathematical theory of communication published in the bell. A history, a theory, a flood by james gleick, the mathematical theory of communication by claude shannon, meta. This book is an updated version of the information theory classic, first published in 1990. If you look up the definition of the word entropy in the dictionary, theres a good chance youll see it defined as a type of energy. Feb 02, 2009 an explanation of entropy in information theory and how to calculate it. Examples are entropy, mutual information, conditional entropy, conditional information, and relative entropy.
Information entropy is occasionally called shannons entropy in honor of claude e. The statistical interpretation is related to the shannon entropy 11, which is used in information theory, and corresponds to the average information density in a system of symbols or atoms. Entropy is particularly friendly to such logical shortcuts. Benfords law the relative frequency of a digit in a file of random numbers in not uniform. Understanding shannons entropy metric for information sriram vajapeyam v. Offers a hardhitting analysis of world turmoil and its ceaseless predicaments, according to the thermodynamic law of entropyall energy flows from order to disorder. In this context, the term usually refers to the shannon entropy, which quantifies the expected value of the. Entropy free fulltext information theory and cognition.
An introduction to information theory and entropy tom carter. A characterization of entropy in terms of information loss john c. Information entropy simple english wikipedia, the free. Information theory a tutorial introduction o information theory. Much of the book is concerned with their properties, especially the long term asymptotic behavior of sample information and expected information. And the entropy of the destination d is defined as the. Lecture notes on information theory and coding mauro barni benedetta tondi 2012. Today, we cover some of the basics of information theory. Given two random variables x and y, we can also define a conditional entropy. Information entropy is the average rate at which information is produced by a stochastic source of data the measure of information entropy associated with each possible data value is the negative logarithm of the probability mass function for the value. While the jones 2 book does not provide a basket full of lemmas and deep insight for doing research on quantifying information, it is a very accessible, tothepoint and selfcontained survey of the main theorems of information theory, and therefore, imo, a good place to start. 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. 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.
Diversityindex entropy is one of several ways to measure diversity. Entropy is defined as a state of disorder or decline into disorder. The information entropy, often just entropy, is a basic quantity in information theory associated to any random variable, which can be interpreted as the average level of information, surprise, or uncertainty inherent in the variables possible outcomes. Understanding shannons entropy metric for information. Please recommend a good philosophical book on entropy.
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