Limit on information density edit information entropy is defined as the logarithm to the base 2 of the number of possible states of a system. The information entropy, often just entropy, is a basic quantity in information theory associated. Negentropy measures the difference in entropy between a given distribution and the gaussian distribution with the same mean and. To take a simple example imagine we have an extremely unfair coin which, when flipped, has a 99% chance of landing heads and only 1% chance of landing tails. Entropy is also a measure of the number of possible arrangements the atoms in a system can have.
Entropy in quantitative thermodynamics is more difficult and often complex. The information content of one of these partial messages is a measure of how much uncertainty. This book is 90% information theory textbook and 10% discussion of entropy and its relation to life. The entropy is the expected value of the selfinformation, a related quantity also introduced by shannon. Shannon defined the entropy of a discrete time discrete alphabet random pro. Equivalently, the shannon entropy is a measure of the average information content one. 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. The book explains with minimum amount of mathematics what information theory is and how it is related to thermodynamic entropy. In information theory, two symbols are necessary and sufficient for an alphabet to be able to encode information, therefore the default is to let b 2 binary entropy.
Here is an intuitive way of understanding, remembering, andor reconstructing shannons entropy metric for information. To conceptualize entropy think of a periodic lattice. 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. 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. Research concerning the relationship between the thermodynamic quantity entropy and the evolution of life began around the turn of the 20th century. Information theory is a subfield of mathematics concerned with transmitting. Information entropy is the average rate at which information is produced by a stochastic source of data.
Its converse is information, which is a measure of order. In this sense, entropy is a measure of uncertainty or randomness. One of the goals of information theory is to estimate the likelihood that one event caused another. Entropy and information theory stanford ee stanford university. At a stroke it explained the nature of matter, all the way from atomic nuclei up to stars. What is an intuitive explanation of the concept of entropy in. 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. The book provides a unified panoramic view of entropy and the second law of thermodynamics.
In information theory, entropy is a measure of the uncertainty associated with a random variable. Entropy is particularly friendly to such logical shortcuts. This format can be read from a web browser by using the acrobat reader helper application, which is available for free downloading from adobe the current version is a. If youre interested in learning about entropy at a more mathematical level, i recommend the excellent textbook thermal physics by daniel schroeder. The closer the q value gets to 1 for the i2 index, the lower the loss would get. As such, we first need to unpack what the term information means in an information theory context. One nat is the amount of information gained by observing an event of probability 1e. However, to begin our qualitative approach we must avoid the briar patches involving the second law and entropy that have been planted all over acres of book pages and web sites. Information theory an overview sciencedirect topics. We explore the history of communication technology leading to the modern field of information theory.
Useful identities and inequalities in information theory are derived and explained. Therefore random mutations by definition cannot be the source of new information in evolution. It was founded by claude shannon toward the middle of the twentieth century and has since then evolved into a vigorous branch. It measures a very important character of random variab. Its a short step to go from understanding entropy to understanding temperature at a more fundamental.
For example i choose that i need information about computers and then two machines gave me information as below. The aim of this book is to explain in simple language what we know and what we do not know about information and entropy two of the most frequently discussed topics in recent literature and whether they are relevant to life and the entire universe. The definition of entropy used in information theory is directly analogous to the definition used in. Added example of probability vs information and more on. Out of all distributions with a given mean and variance, the normal or gaussian distribution is the one with the highest entropy. Popular entropy books meet your next favorite book. The historical and theoretical foundations of thermodynamics authors. In this post, you discovered a gentle introduction to information entropy.
However, the concept of shanon entropy shares some intuition with boltzmanns. Karel capek, krakatit this strange word denotes one of the most basic quantities of the physics of heat phenomena, that is, of thermodynamics. Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel. Our definition of i x is therefore written in units of nats. 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. Because of its dependence on ergodic theorems, however, it can also be viewed as a branch of ergodic theory, the theory of invariant transformations and transformations related to invariant transformations. Although the concept of entropy did indeed originate in thermodynamics, it later became clear that it was a more.
The higher the entropy of an object, the more uncertain we are about the states of the atoms making up that object. To do so, the transmitter sends a series possibly just one partial messages that give clues towards the original message. It is the expectation value of the self information log px. These developments simultaneously explained how string theory is related to some forms of supersymmetric quantum field theories.
Apr 26, 2014 16 videos play all information theory, pattern recognition, and neural networks jakob foerster a short introduction to entropy, crossentropy and kldivergence duration. Entropy information theory, entropy in thermodynamics and information theory and entropic uncertainty. An introduction to entropy, cross entropy and kl divergence. Willard gibbs in 1878 after earlier work by boltzmann 1872. This definition is essentially due to shannon in 1948, in the seminal papers in. The notion of entropy, which is fundamental to the whole topic of this book, is introduced here. A cornerstone of information theory is the idea of quantifying how much information there is in a message.
Shannons entropy leads to a function which is the bread and butter. Finally we arrive at our quantitative measure of entropy. 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. Entropy is the average rate of information produced from a certain stochastic process see here. When viewed in terms of information theory, the entropy state function is simply the amount of information in the shannon sense that would be needed to specify the full microstate of the system. We have also explained that thermodynamic entropy and the entropy of information theory are the same in terms of increasing randomness. The measure of information entropy associated with each possible data value is the negative logarithm of the probability mass function for the value. Informationentropyisthelogbase2of thenumberofpossibleoutcomes. A history, a theory, a flood by james gleick, the mathematical theory of communication by claude shannon, meta. The definition of entropy for a probability distribution from the deep learning book. Well build up towards claude shannons measure of information entropy, one step at a time. 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.
Entropy shows up in a wide variety of contexts including physics, information theory and philosophy. Information theory is the mathematical treatment of the concepts, parameters and rules governing the transmission of messages through communication systems. There has to be a different explanation for evolution. Conceptually, information can be thought of as being stored in or transmitted as variables that can take on different values. We can quantify the amount of uncertainty in an entire probability distribution using the shannon entropy. To some theorists, though, information is more than just a description of our universe and the stuff in it. The shannonweaver book makes reference to tolman 1938 who in turn credits pauli 1933 with the definition of entropy shannon. Social entropy theory illuminates the fundamental problems of societal analysis with a nonequilibrium approach, a new frame of reference built upon contemporary macrological principles, including general systems theory and information theory. The entropy of an object is a measure of the amount of energy which is unavailable to do work.
The information content of one of these partial messages is a measure of how much uncertainty this resolves for the receiver. The information entropy which has been removed from a system where information is stored is a tiny subset of the thermodynamic entropy, and you can only reliably store information in parts of a system which are effectively at zero temperature. Entropy shows up in a wide variety of contexts including physics, information theory and. Information theory seeks to understand the influences of different parts of a system on one another by comparing their entropies, or conversely by comparing their informations.
The fundamental idea is that, if the entropy of an information source drops, that means we can ask fewer questions to guess the outcome. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated using probability. Information entropy, which is a measure of information communicated by systems that are affected by data noise. The intuition behind shannons entropy towards data science. 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. 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. What is an intuitive explanation of the concept of entropy. The meaning of entropy is different in different fields. This post is my take on the ideas in chapter 2 of his book and also summarized in this paper. This book is devoted to the theory of probabilistic information measures and. Information theory was born in a surprisingly rich state in the classic papers of claude e. Social entropy theory, using shannons h and the entropy concept, avoids the common and often. In information theory, the major goal is for one person a transmitter to convey some message over a channel to another person the receiver.
I believe a good intuitive explanation enables you to apply a concept without the mental overhead of too many mathematical details. Nonfiction book by jeremy rifkin and ted howard, with an afterword by nicholas georgescuroegen. This is a fascinating subject, which arose once the notion of information got precise and quantifyable. Noise is information entropy which is the irreversible destruction of information. Jk in thermodynamics in information theory, 1ln2 k bit, or 1 nat, are chosen, instead. Information theory is concerned with data compression and transmission and builds upon probability and supports machine learning. Along the way, well give some intuitive reasoning behind these values in addition to the formulas. Entropy is commonly interpreted as a measure of disorder. Entropy is maximum when all outcomes are equally likely. Entropy is simply a quantitative measure of what the second law of thermodynamics describes. Fuzzy rational foundations of information knowledge certainty english isbn. We have also explained that thermodynamic entropy and the entropy of information theory are the.
Information theory can be viewed as simply a branch of applied probability theory. This interpretation has caused a great amount of disorder in the literature. Social entropy theory, using shannons h and the entropy concept, avoids the common and often artificial separation of. Thus, the entropy of the source alphabet, with its given empiric probability distribution, is a number equal to the number possibly fractional of symbols of the ideal. This is because the kl divergence between p and q is reducing for this index. What shannon did was to attempt to quantify the amount of information that bob transfers to alice. Understanding shannons entropy metric for information. Is information entropy the same as thermodynamic entropy. An introduction to information theory and entropy tom carter. Any time you move away from equally likely outcomes, or introduce predictability, the entropy must go down. A mathematical theory of communication markov text.
Last updated on november 7, 2019 information theory is a subfield of read more. This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The following discussion has been partly derived from the second edition of the book science and information theory by leon brillouin 1 as well as from the book an introduction to information theory by john r. We need only specify the locations of the sites in a singl.
Shannons metric of entropy of information is a foundational concept of information theory 1, 2. Shannon 1 2 which contained the basic results for simple memoryless sources and channels and introduced more general communication systems models, including nite state sources and channels. Sep 14, 2012 we explore the history of communication technology leading to the modern field of information theory. Information theory is the mathematical treatment of the concepts, parameters and rules governing the. From a physical point of view, information theory has nothing to do with physics. 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. Entropy simple english wikipedia, the free encyclopedia. Entropy is the information required to specify the state of the system. Today, we cover some of the basics of information theory. Shannon entropy this chapter is a digression in information theory. 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.
More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated. The concept of information entropy was introduced by claude shannon in his 1948 paper a mathematical theory of communication. 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. Apr 09, 2016 entropy is the information required to specify the state of the system. One of the aims of this book is to put some order in this disorder. Extracareis taken in handlingjointdistributions withzeroprobability masses. The authors argue that humanity is wasting resources at an increasing rate, and that will lead to the destruction of our. We have shown that the ordinary use of the word information is much different from the word information in information theory.
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