Information theory an overview sciencedirect topics. What is an intuitive explanation of the concept of entropy in. 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 bit s. Shannon entropy has been related by physicist leon brillouin to a concept sometimes called negentropy. An elegant way to work out how efficient a code could be, it. The first part of this paper will deal with the mathematics and derivation of a formula for spatial entropy, which will then be applied to some. Entropy in thermodynamics and information theory wikipedia. 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.
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. In 1910, american historian henry adams printed and distributed to university libraries and history professors the small volume a letter to american teachers of history proposing a theory of history based on the second law of thermodynamics and on. This book is devoted to the theory of probabilistic information measures and. Gray information systems laboratory electrical engineering department stanford university springerverlag new york c 1990 by springer verlag. If you have more than 2 labels, you can generalize the entropy formula as follows. It is certainly appropriate that this paper begins with an overview of shannon entropy.
The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of thermodynamics is not an. Research concerning the relationship between the thermodynamic quantity entropy and the evolution of life began around the turn of the 20th century. Reversible processes do not increase the entropy of the universe. Shannons entropy leads to a function which is the bread and butter. From a physical point of view, information theory has nothing to do with physics.
Entropy and information theory stanford ee stanford university. The calculation of information is often written as h. To do so, the transmitter sends a series possibly just one partial messages that give clues towards the original message. In 1953, brillouin derived a general equation stating that the changing of an information bit value requires at least kt ln 2 energy. Our definition of i x is therefore written in units of nats.
The defining expression for entropy in the theory of statistical mechanics established by ludwig boltzmann and j. Digital communication information theory tutorialspoint. The shannonweaver book makes reference to tolman 1938 who in turn credits pauli 1933 with the definition of entropy shannon. The chapter begins with the short description about the concept of entropy, formula, and matlab code. Short introduction to the axioms of information theory, entropy, mutual information, kullbackliebler divergence, and jensenshannon distance. Information, entropy and their geometric structures. Consider a simple digital circuit which has a twobit input x, y and a twobit output x and y, x or y. But suppose that, instead of the distribution of characters shown in the table, a long series of as were transmitted. But shannon wasnt thinking about people talking to each other. Developed by claude shannon and norbert wiener in the late 1940s, information theory, or statistical communication theory, deals with the theoretical underpinnings of a wide range of communication devices. Entropy in information theory second part on entropy.
Information entropy is occasionally called shannons entropy in honor of claude e. Information theory is the mathematical treatment of the concepts, parameters and rules governing the. Shannons work was like einsteins gravitation theory, in that he created the whole field all at once, answering the most important questions at the beginning. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated using probability. What is the role of the logarithm in shannons entropy. 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. In 1910, american historian henry adams printed and distributed to university libraries and history professors the small volume a letter to american teachers of history proposing a theory of history based on the second law. Diversityindex entropy is one of several ways to measure diversity. Entropy in statistical physics proof of the ideal gas law. However, the concept of shanon entropy shares some intuition with boltzmanns.
One nat is the amount of information gained by observing an event of probability 1e. An introduction to entropy, cross entropy and kl divergence. Its not very often that a single paper opens up a whole new science. The definition of entropy used in information theory is directly analogous to the definition used in. Karel capek, krakatit this strange word denotes one of the most basic quantities of the physics of heat phenomena, that is, of thermodynamics. Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system. The rebus principle is introduced via cave drawings, narmer palette, hunters palette, cuneiform accounting tablets. 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. Online tool for calculating entropy plain text entropy online tool for calculating entropy binary notes and references.
This is a fascinating subject, which arose once the notion of information got precise and quantifyable. Equivalently, the shannon entropy is a measure of the average information content one. The closer the q value gets to 1 for the i2 index, the lower the loss would get. This book is 90% information theory textbook and 10% discussion of entropy and its relation to life. The file compression problem imagine a list of separate elementary systems say, molecules. The definition of entropy for a probability distribution from the deep learning book. An introduction to information theory and entropy iis windows server. If we consider an event, there are three conditions of occurrence. The inspiration for adopting the word entropy in information theory came from the close resemblance between shannons formula and very similar known formulae from statistical mechanics. An analog to thermodynamic entropy is information entropy. The defining expression for entropy in the theory of information established by claude e. See more ideas about information theory, what is information and entropy definition. The concept of entropy provides deep insight into the direction of spontaneous.
Within the main chapter body, three different approaches how to use the information entropy in dataset analysis. Benfords law the relative frequency of a digit in a file of random numbers in not uniform. Black hole entropy is a concept with geometric root but with many physical consequences. 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. 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. Information theory is a mathematical approach to the study of coding of information along with the quantification, storage, and communication of information conditions of occurrence of events. A simple explanation of entropy in decision trees benjamin. Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel.
Entropy is particularly friendly to such logical shortcuts. Applications of informationentropy geometric structures ali mohammaddjafari entropy, information theory, information geometry and bayesian inference in data, signal and image processing and inverse problems reprinted from. Entropy, the measure of a systems thermal energy per unit temperature that is unavailable for doing useful work. Information theory is a mathematical approach to the study of coding of information along with the quantification, storage, and communication of information. You may use different kinds of entropies, have a look at renyi entropy. H as the negative of a certain sum involving probabilities. Shannons information, information entropy avoid confusion with with thermodynamical entropy shannons entropy formula. In 1948, while working at bell telephone laboratories electrical engineer claude shannon set out to mathematically quantify the statistical nature of lost information in phoneline signals. The use of information theory was introduced in statistics bykullback and leibler1951 and developed by kullback in his book kullback,1959. I believe a good intuitive explanation enables you to apply a concept without the mental overhead of too many mathematical details. Nevertheless, some authors argue for dropping the word entropy for the h function of information theory and using shannons other term uncertainty instead. Today, we cover some of the basics of information theory.
In statistical thermodynamics the most general formula for the thermodynamic entropy s of a thermodynamic system is the gibbs entropy. Although the concept of entropy did indeed originate in thermodynamics, it later became clear that it was a more. The thermodynamic state of a system is characterised by the values of its thermodynamic variables. We can compute or measure the quantity of energy contained in this sheet of paper, and the same is true of its entropy. In information theory, entropy is a measure of the uncertainty associated with a random variable. The term information theory refers to a remarkable field of study developed by claude shannon in 1948. 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 notion of entropy, which is fundamental to the whole topic of this book, is introduced here. In statistics, entropy will be interpreted as a measure of uncertainty or of risk. This is because the kl divergence between p and q is reducing for this index. However, a more modern based on information theory treats entropy as uncertainty.
Entropy and information theory first edition, corrected robert m. Statistical entropy and information theory physics stack. Shannon entropy this chapter is a digression in information theory. Information theory from the diaries of john henry medium. This is the same energy as the work leo szilard s engine produces in the idealistic case, which in turn. Its title may seem strange at first human communication is everything but mathematical.
Rifkins 1980 views assume that entropy is disorder. Understanding shannons entropy metric for information. It is a generalization of the standard entropy shannons entropy. What is an intuitive explanation of the concept of entropy. Although the form of both equations definning entropy seems similar, shannon entropy has its motivations from information theory. The bekensteinhawking entropy or black hole entropy is the amount of entropy that must be assigned to a black hole in order for it to comply with the laws of thermodynamics as they are interpreted by observers external to that black hole. This book goes weaver, in the 1949 book form of shannons paper where weaver was tapped to write a mostly prose explanation. Finally we arrive at our quantitative measure of entropy. We can quantify the amount of uncertainty in an entire probability distribution using the shannon entropy. Information i in information theory is generally measured in bits, and can loosely, yet instructively, be defined as the amount of surprise arising from a given event.
Information theory is a subfield of mathematics concerned with transmitting. Apr 30, 2016 t his equation was published in the 1949 book the mathematical theory of communication, cowritten by claude shannon and warren weaver. The concept of information entropy was introduced by claude shannon in his 1948 paper a mathematical theory of communication. It measures a very important character of random variab. A mathematical theory of communication, ascii code, binary digit, bits per character, claude shannon, compression, data compression, david huffman, entropy, entropy english language, entropy in a coin flip, entropy per character, huffman code, increase in knowledge, information content, information entropy. Information theory studies the quantification, storage, and communication of information. Shannon, who formulated many of the key ideas of information theory. It was founded by claude shannon toward the middle of the twentieth century and has since then evolved into a vigorous branch. Introduction the concept of entropy in information theory describes how much information there is in a signal or event.
Here is an intuitive way of understanding, remembering, andor reconstructing shannons entropy metric for information. The information content of one of these partial messages is a measure of how much uncertainty this resolves for the receiver. What shannon did was to attempt to quantify the amount of information that bob transfers to alice. In information theory, the major goal is for one person a transmitter to convey some message over a channel to another person the receiver. History of entropy project gutenberg selfpublishing. T his equation was published in the 1949 book the mathematical theory of communication, cowritten by claude shannon and warren weaver. Our galaxy, the solar system, and the biosphere all take their being from entropy, as a result of its transferenceto the surrounding medium. Recall that the table comparison of two encodings from m to s showed that the second encoding scheme would transmit an average of 5. In his 1962 book science and information theory, brillouin described the negentropy principle of information or npi, the gist of which is that acquiring information about a systems microstates is associated with a decrease in entropy work is needed to extract information, erasure leads to increase in thermodynamic entropy. The intuition behind shannons entropy towards data science. Examples are entropy, mutual information, conditional entropy, conditional information, and relative entropy discrimination, kullbackleibler. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated. There are many ways of demonstrating the equivalence of information entropy and physics entropy, that is, the equivalence of shannon entropy and boltzmann entropy.
A cornerstone of information theory is the idea of quantifying how much information there is in a message. Whats worse is the author then goes about slamming the ideas of erwin schrodinger, which is im sure the reason a substantial amount of potential readers by the book, in the least elequent, least substatiated fashion i can imagine from someone well versed in this area. The inspiration for adopting the word entropy in information theory came from the close resemblance between shannons formula and very similar known formulae from thermodynamics in statistical thermodynamics the most general formula for the thermodynamic entropy s of a thermodynamic system is the gibbs entropy. The book promotes the use of sustainable energy sources and slow resource consumption as the solution to delay or forestall death by entropy. This book is an excellent introduction to the mathematics underlying the theory.
But thats what happened in 1948 when claude shannon published his mathematical theory of communication. Shannons metric of entropy of information is a foundational concept of information theory 1, 2. Information is the source of a communication system, whether it is analog or digital. Entropy is a mathematical formula jozsef garai email. Entropy is related to the concept of weight of evidence from information theory note this is not the same as discussed here intuition behind weight of evidence and information value formula. Although contextually different, these two entropies imply physically similar situations, the boltzmann factor however comes due to the logarithmic base conversion. Popular entropy books meet your next favorite book.
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