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Topic: Information entropy

Related Topics

Information theory

Entropy

Thermodynamic entropy

Probability distribution

Mutual information

Binomial distribution

Bernoulli distribution

Multinomial distribution

Maximum likelihood

Fisher information

Normal distribution

Exponentiation

Probability density function

	NationMaster - Encyclopedia: Information entropy
		In information theory, the Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable.
		Information entropy is occasionally called Shannon's entropy in honor of Claude E. Shannon, who formulated many of the key ideas of information theory.
		Entropy is a measure of this randomness, suggested by Claude E. Shannon in his 1949 paper A Mathematical Theory of Communication.
	www.nationmaster.com /encyclopedia/Information-entropy (571 words)

	Information entropy to measure temporal and spatial complexity of unsaturated flow in heterogeneous media
		Information entropy to measure temporal and spatial complexity of unsaturated flow in heterogeneous media
		In this paper, we evaluate the complexity of these behaviors using information entropy.
		As an example, we use information entropy to evaluate the temporal and spatial complexity of simulated flow processes invoked by infiltration into heterogeneous porous media.
	www.agu.org /pubs/crossref/2002/2001WR001185.shtml (298 words)

	Kids.Net.Au - Encyclopedia > Information entropy
		Entropy as defined by Shannon is closely related to entropy as defined by physicists.
		The entropy of English text is about 1.5 bits per character (Try compressing it with the PPM compression algorithm[?]!) The entropy rate of a data source means the average number of bits per symbol needed to encode it.
		Entropy is effectively the lowest compression possible, which can be realised in theory by the use of the typical set or in practise using Huffman, Lempel-Ziv or Arithmetic coding.
	www.kids.net.au /encyclopedia-wiki/in/Information_entropy (445 words)

	PlanetMath: Shannon's entropy (Site not responding. Last check: )
		Entropy is maximized when the probability distribution is uniform.
		Entropy in the continuous case is called differential entropy.
		This is version 21 of Shannon's entropy, born on 2001-11-19, modified 2006-06-28.
	planetmath.org /encyclopedia/Entropy.html (486 words)

	information entropy (Site not responding. Last check: )
		Entropy is a concept in thermodynamics (see thermodynamic entropy), statistical mechanics and information theory.
		It thus served as a proxy capturing the concept of information contained in a message as opposed to the portion of the message that is strictly determined (hence predictable) by inherent structures.
		The entropy rate of a data source means the average number of bits per symbol needed to encode it.
	www.abacci.com /wikipedia/topic.aspx?cur_title=information_entropy (683 words)

	Thermodynamic Entropy and Information
		Information is a measure of how much an image/message (an observed micro-state) tells us, by comparison with the number of other messages it could have been (those consistent with the image/message's macro-state).
		Entropy refers to the uncertainty of an unknown message, and information refers to the probability of a known message occurring by chance alone.
		More accurately, entropy is a measure of uncertainty due to the unknown part of a message/particle system, and information is a measure of reduction of uncertainty due to the known part of a message/particle system.
	lcni.uoregon.edu /~mark/Stat_mech/thermodynamic_entropy_and_information.html (1464 words)

	The Paradox of Truth, the Truth of Entropy
		Thermodynamic entropy is the measure of this disorganization in the universe.
		Information theory is the mathematical theory of communication that is used to find out the speed and quantity of information transmission.
		The Demon has the power to "somehow" reverse thermodynamic entropy, by producing a "staggering set of energies" through the destruction of a "massive complex of information." His actions would violate the second law of thermodynamics, because entropy is an irreversible transformation.
	www.pynchon.pomona.edu /entropy/paradox.html (2297 words)

	The Entropy System™ - BSI Entropy - Solutions
		Entropy Software is a market-leading web-based solution for enterprise-level risk, compliance and performance management.
		Entropy Software allows users to add and integrate any number of risk disciplines iinto their management process and provides a complete framework for managing risk across an organization.
		Entropy Software is composed of five key workflows which work across risk areas for a comprehensive view.
	www.bsi-entropy.com /solutions (405 words)

	Information Is Not Uncertainty
		Information is always a measure of the decrease of uncertainty at a receiver (or molecular machine).
		Shannon's 1948 paper, it seems to be suggested, that part of the received information is due to noise.
		This is obviously a slip of the pen of Shannon, as he merely tries to explain, in words, that the information rate R is the initial uncertainty minus the uncertainty due to the noise; but he calls H "information" instead of "entropy".
	www.lecb.ncifcrf.gov /~toms/information.is.not.uncertainty.html (859 words)

	JCE 1999 (76) 1385 [Oct] Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms - Examples of Entropy Increase? ...
		Entropy is increased in the shuffler's and in the billiard cue holder's muscles, in the tornado's wind and the earthquake's stressnot in the objects shifted.
		The point is that information "entropy" in all of its myriad nonphysicochemical forms as a measure of information or abstract communication has no relevance to the evaluation of thermodynamic entropy change in the movement of macro objects because such information "entropy" does not deal with microparticles whose perturbations are related to temperature.
		It is the presence of temperature in R that distinguishes physical entropy from all information "entropy".
	jchemed.chem.wisc.edu /Journal/Issues/1999/Oct/abs1385.html (2476 words)

	Information Theory and Creationism: Classical Information Theory (Shannon)
		That is, the information source is assumed to be a random process, outputing a sequence of symbols from a fixed symbol set, where the probability of each new symbol depends on only on the preceding symbol.
		Entropy in information theory does not mean information is becoming more useless or degraded; and because it is a mathematical abstraction, it does not directly relate to physical work unless you are treating molecules informatically.
		Science and Information Theory, Brillouin described the Negentropy Principle of Information or NPI, the gist of which is that acquiring information about a system’s microstates is associated with a decrease in entropy (work is needed to extract information, erasure leads to increase in thermodynamic entropy).
	www.talkorigins.org /faqs/information/shannon.html (3369 words)

	Life, information, entropy, and time
		Information content is encoded in a physical system through an ordering that requires input of work, and the term is then used as a synonym for the increase in order (negentropy) in its standard physical sense.
		Information is encoded in the local gradients, physical or chemical, that define the state of each coding element, and the effectiveness of storage is directly related to the stability of the gradients formed.
		The utility of informational entropy lies in the fact that two encoded messages, before and after transmission for example, can be compared in the context of the coding elements, even when the encoding is different.
	www.life.uiuc.edu /crofts/papers/Life_information_entropy_and_time.html (8207 words)

	Information theory - EvoWiki (Site not responding. Last check: )
		What Boltzmann, who was the first to equate entropy with disorder, meant was that increasing entropy in a system corresponds with increasing unpredictability of the internal state of that system.
		Mutations in a message may add information that is not desirable to the receiver; in fact, in biotic systems this is generally the case.
		Note that the entropy function depends on the instruction set of the processing machine and is in general not a computable function – meaning that there is no program E that given a string S as input is guaranteed to halt, if E tries to compute H(S).
	wiki.cotch.net /index.php/Information (2482 words)

	welcome to entropysite.com
		In the October 2002 Journal I urged that entropy be presented as the quantity of dispersal of energy/T or by the change in the number of microstates.
		"Entropy is disorder" is an archaic, misleading definition of entropy dating from the late 19th century before knowledge of molecular behavior, of quantum mechanics and molecular energy levels, or of the Third Law of thermodynamics.
		Entropy may be the most feared topic in beginning university chemistry — by students because of its complexity, by instructors because students fail to understand its basic principles.
	www.entropysite.com (5071 words)

	Entropy - An Open-Access Journal on Entropy and Information Studies
		Entropy, an International and Interdisciplinary Journal of Entropy and Information Studies.
		Entropy is indexed and abstracted by Chemical Abstracts, INSPEC (covered completely, see the list) and Scopus.
		Important additional information: All thematic special issues will be fully Open Access with publishing fees paid by authors or their institutes.
	www.mdpi.org /entropy (287 words)

	Shuffled cards
		Entropy is increased in the shuffler's and in the billiard cue holder's muscles, in the tornado's wind and the earthquake's stress — not in the objects shifted.
		This is not to say that the extremely general mathematics of information theory cannot be modified ad hoc and further specifically constrained to yield results that are identical to Gibbs' or Boltzmann's relations [6].
		It has been said that an information "entropy" equation — compared to those for thermodynamic entropy — may look like a duck but, without any empowering thermal energy, it can't quack like a duck or walk like a duck.
	www.entropysite.com /shuffled_cards.html (2812 words)

	Good Math, Bad Math : An Introduction to Information Theory (updated from Blogspot)
		Shannon called the information content of a signal it's entropy, because he saw a similarity between his information entropy and thermodynamic entropy: in a communicating system, entropy never decreases: it increases until the capacity of the channel is reached, and then it stays content.
		Entropy is a property of a source (a random variable), not a signal.
		Meaning is a separate question; information quantity is about "how much can be coded into a string of a certain length"; it doesn't matter whether what you're coding is a string of random bits, or the decay times of a collection of radioactive atoms, or the complete works of shakespear.
	scienceblogs.com /goodmath/2006/06/an_introduction_to_information.php (4568 words)

	An Intuitive Explanation of the Information Entropy of a Random Variable (Site not responding. Last check: )
		Information about the point's vertical position has no effect on the outcome, so we just ignore it; it is part of the information that is irretrievably lost.
		"entropy" of a random variable is the same formula as the expected value with the Value filled in with the Information.
		relative entropy of a question is the entropy given what you also already know.
	www.cs.berkeley.edu /~dsw/entropy.html (3251 words)

	Entropy Dashboard Widget (Site not responding. Last check: )
		Entropy uses true-random bytes from a variety of sources of entropy, including radioactive decay (HotBits random data server at fourmilab.ch), atmpospheric noise (Random.org random byte generator), the EntropyPool and your Mac's own /dev/random.
		For an introduction to the concept of entropy in information theory, or the phenomenon of true-randomness, read this essay at random.org.
		Entropy no longer uses a proxy server between itself and the HotBits server (a set up that was responsible for HotBits' 'quota exceeded' errors due to all requests coming from the same IP address).
	entropy.myvnc.com (225 words)

	Entropy and Information
		This difference can also be interpreted in a different way, as information, and historically H was introduced by Shannon as a measure of the capacity for information transmission of a communication channel.
		H has been vigorously pursued as a measure for a number of higher-order relational concepts, including complexity and organization.
		We also note that there are other methods of weighting the state of a system which do not adhere to probability theory's additivity condition that the sum of the probabilities must be 1.
	pespmc1.vub.ac.be /ENTRINFO.html (471 words)

	Marc Liyanage - Software - Mac OS X Packages - PHP
		You should see a status table with information about the PHP module.
		Some of them are rather old and might not be appropriate for current OS X and PHP package releases so if in doubt you should check the forum for the most up-to-date information.
		Carsten Klapp has some information about activating PEAR for version 4.1 of the module
	www.entropy.ch /software/macosx/php (1645 words)

	Energy Citations Database (ECD) - - Document #20665064
		S is the sum of the information entropies in position and momentum spaces.
		It is found that, for three different Fermi systems with different particle interactions, the correlated part of S (S{sub cor}) depends on the correlation parameter of the systems or on the discontinuity gap of the momentum distribution through two parameter expressions.
		The study of thermal effects on the uncorrelated electron gas leads to a relation between the thermal part of S (S{sub thermal}) and the fundamental quantities of temperature, thermodynamical entropy, and the mean kinetic energy.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20665064&query_id=0 (373 words)

	ENTROPY
		Entropy is a quantity that, in its two contexts, characterizes not only all form and life in the universe, but all signal, language, information and written material ever produced anywhere.
		It uses statistical concepts of probability to compute the extra information (redundancy) necessary to counteract the distortion and losses that may occur during transmission from one information source to another.
		Another consequence of the second law of thermodynamics, is that the entropy, or disorder, of the universe must increase for a reaction or event to occur (thus over time the universe proceeds toward the most probable state--hypothetically a "heat-death" of complete uniformity as mentioned by Pynchon in "Entropy").
	www.pynchon.pomona.edu /entropy/index.html (2066 words)

	Thermodynamic entropy vs information entropy - Advanced Physics Forums (Site not responding. Last check: )
		The information entropy is the log of the number of accesible states, and is dimensionless.
		For informational entropy, the number of accessible states would be the number of different possible words, which I think would be 2^n, where n is the number of bits.
		Useful information that was propagating down the wire was lost in the sense that it became random thermal motion, but the information is still there at the microscopic level in the sense that more knowledge is now required to describe the microscopic state of the system.
	www.advancedphysics.org /forum/showthread.php?t=5031 (3088 words)

	Entropy in Information and Coding Theory
		In 1948, motivated by the problem of efficiently transmitting information over a noisy communication channel, Claude Shannon introduced a revolutionary new probabilistic way of thinking about communication and simultaneously created the first truly mathematical theory of entropy.
		His ideas created a sensation and were rapidly developed along two main lines of development: information theory, which employs probability and ergodic theory to study the statistical characteristics of data and communication systems, and coding theory, which uses mainly algebraic and geometric tools to contrive efficient codes for various situations.
		Focuses on the contrast between the traditional interpretation of the entropy of a stationary ergodic source in terms of the number of typical sequences of a given length and the interpretation in terms of the recurrence of blocks of symbols ("patterns") in a single typical sequence.
	www.math.uni-hamburg.de /home/gunesch/Entropy/infcode.html (1024 words)

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