About entropy in thermodynamics entropy in information theory Entropy information theory a comparison of entropy in information theory with entropy in thermodynamics Entropy in thermodynamics and information theory other uses Entropy disambiguation See introduction File Ice water.jpg thumb Ice melting in a warm room is a common Entropy Ice melting example example of increasing entropy, ref group note ... or when salt is added to an ice water mixture, entropy can either increase or decrease depending ... of a supercooled liquid takes place under adiabatic conditions the entropy of the resulting crystal ... Equilibrium , 4th Ed. . In general, however, when ice melts, the entropy of the two adjoined systems ... CCA CCA3 MAIN ENTROPY PAGE1.HTM Ice melting JCE example http www.bartleby.com 64 C004 024.html Ice melting and Entropy Change example http www.ac.wwu.edu vawter PhysicsNet Topics ThermLaw2 Entropy InterptEntropy.html Ice melting and Entropy Change discussions ref described in 1862 by Rudolf Clausius ..., S. 2. vol. vii. p. 209. ref EntropySegments Entropy is a List of thermodynamic properties thermodynamic ... to work. During this work, entropy accumulates in the system, which then dissipation dissipates in the form of waste heat . In classical thermodynamics, the concept of entropy is defined Phenomenology science phenomenologically by the second law of thermodynamics , which states that the entropy .... Thus, entropy is also a measure of the tendency of a process, such as a chemical reaction, to be entropically ... of heat . These processes reduce the state of order of the initial systems, and therefore entropy ... of entropy in statistical mechanics , where entropy is defined as the amount of additional ... postulate fundamental postulate of statistical mechanics . Thermodynamic entropy has the dimension ... of Units . The term entropy was coined in 1865 by Rudolf Clausius based on the Greek entrop a ... www.etymonline.com index.php?term entropy title Entropy publisher Online Etymology Dictionary accessdate ... more details
Maximum entropy may refer to The principle of maximum entropy The maximum entropy probability distribution Maximum entropy spectral estimation Maximum entropy spectral analysis Maximum entropy thermodynamics The law of maximum entropy production Entropy maximization Maximum entropy classifier See also Second law of thermodynamics also known as the law of increasing entropy disambig ... more details
wiktionarypar entropy div class infobox sisterproject Additional relevant articles may be found in the following categories Category Thermodynamic entropy Thermodynamic entropy Category Entropy and information Entropy and information Category Quantum mechanical entropy Quantum mechanical entropy div Entropy , in thermodynamics, is a measure of the energy in a thermodynamic system not available to do useful work. Entropy may also refer to Thermodynamics Entropy classical thermodynamics , the macroscopic approach to thermodynamic entropyEntropy energy dispersal , a variant perspective on thermodynamic entropyEntropy statistical thermodynamics , the microscopic approach to thermodynamic entropy Gibbs entropy , statistical entropy of a thermodynamic system Boltzmann entropy , an approximation to Gibbs entropy Tsallis entropy , a generalization of Boltzmann Gibbs entropy von Neumann entropy , entropy of a quantum mechanical system Entropy order and disorder , entropy s association with the amount of order, disorder, and or chaos in a thermodynamic system History of entropy , concept of entropy ... Introduction to entropyEntropy and life , research concerning the relationship between the thermodynamic quantity entropy and the evolution of life Entropy astrophysics , the adiabatic constant Entropy arrow of time , thermodynamic arrow of time Information theory and mathematics Entropy information theory , a measure of the amount of information contained in a message Entropy encoding , data compression strategies to produce a code length equal to the entropy of a message Kolmogorov Sinai entropy , the rate of information generation by a measure preserving dynamical system R nyi entropy , a family of diversity measures used to define fractal dimensions Topological entropy , a measure of exponential growth in the number of distinguishable orbits of a dynamical system Volume entropy ... science Entropy computing , a discussion of entropy generation and API s in computer systems Entropy ... more details
unreferenced date September 2011 Entropy is considered to be an extensive property, i.e., that its value depends on the amount of material present. Constantino Tsallis has proposed a nonextensive entropy , which is a generalization of the traditional Boltzmann Gibbs entropy . The rationale behind the theory is that Gibbs Boltzmann entropy leads to systems that have a strong dependence on initial conditions . In reality most materials behave quite independently of initial conditions. Nonextensive entropy leads to nonextensive statistical mechanics , whose typical functions are power law s, instead of the traditional exponential s. See also Tsallis entropy Statistical mechanics topics Category Probability theory Category Entropy and information Category Thermodynamic entropy Category Information theory condensedmatter stub ... more details
original research date March 2012 unreferenced date March 2012 Weighted entropy is a notion which extends the classical Shannon entropy. Category Information theory ... more details
Unreferenced stub auto yes date December 2009 The entropy of vaporization is the increase in entropy when vaporizing a substance. This is always positive since the EntropyEntropy as a measure of disorder degree of disorder increases in the phase transition transition from an organized crystal line solid or a slightly less organized liquid to the extremely disorganized structure of a gas . It is denoted as S sup s o s sup sub vap sub and normally expressed in Joule J mole unit mol Kelvin K . Entropy of vaporisation is denoted by Sfg. In a phase change , both phases coexist in a equilibrium, so the Gibbs free energy is equal to zero. It follows that the entropy of vaporization is related to the boiling point and the enthalpy of vaporization math Delta H vap T vap times Delta S vap math See also Entropy of fusion Trouton s rule DEFAULTSORT Entropy Of Vaporization Category Thermodynamic entropy Category Thermodynamic properties Chem stub ar de Verdampfungsentropie it Entropia di vaporizzazione ... more details
Orphan date January 2011 Infobox journal title Entropy cover Image Entropy logo.png discipline Physics , chemistry abbreviation Entropy publisher MDPI country frequency Monthly history 1999 present openaccess Yes website http www.mdpi.com journal entropy ISSN 1099 4300 Entropy is a Peer review peer reviewed open access scientific journal on entropy and information studies . It was established in 1999 and is published by MDPI . According to the Journal Citation Reports , the journal has a 2010 impact factor of 1.109. ref name WoS cite book year 2011 chapter Entropy title 2010 Journal Citation Reports publisher Thomson Reuters edition Science accessdate 2011 09 15 work Web of Science postscript . ref References Reflist External links Official http www.mdpi.com journal entropy Category Physics journals Category Chemistry journals Category Open access journals Category Multidisciplinary Digital Publishing Institute academic journals Category Monthly journals Category English language journals Category Publications established in 1999 fr Entropy journal ... more details
Mergeto Entropy statistical thermodynamics date July 2009 In thermodynamics , specifically in statistical mechanics , the Boltzmann entropy is an approximation to the normal Gibbs entropy . The Boltzmann entropy is obtained if one assumes one can treat all the component particles of a thermodynamic system as statistically independent. The probability distribution of the system as a whole then factorises into the product of N separate identical terms, one term for each particle and the Gibbs entropy simplifies to the Boltzmann entropy math S B N k B sum i p i log p i , math where the summation is taken over each possible state in the 6 dimensional phase space of a single particle rather than the 6 N dimensional phase space of the system as a whole . This reflects the original statistical entropy function introduced by Ludwig Boltzmann in 1872 . For the special case of an ideal gas it exactly corresponds to the proper entropy thermodynamic entropy . However, for anything but the most dilute of real gases, it leads to increasingly wrong predictions of entropies and physical behaviours, by ignoring the interactions and correlations between different molecules. Instead one must follow Gibbs, and consider the statistical ensemble ensemble of states of the system as a whole, rather than single particle states. See also EntropyEntropy thermodynamics Boltzmann s entropy formula Gibbs entropy References reflist E.T. Jaynes Jaynes, E. T. 1965 . http bayes.wustl.edu etj articles gibbs.vs.boltzmann.pdf Gibbs vs Boltzmann entropies . American Journal of Physics , 33 , 391 8. External links DEFAULTSORT Boltzmann Entropy thermodynamics stub Category Thermodynamic entropy Category Article Feedback 5 ... more details
In probability theory or information theory , the min entropy of a discrete random event x with possible states or outcomes 1... n and corresponding probabilities p sub 1 sub ... p sub n sub is math H infty X min i 1 n log p i max i log p i log max i p i math The base of the logarithm is just a scaling constant for a result in bit s, use a base 2 logarithm. Thus, a distribution has a min entropy of at least b bits if no possible state has a probability greater than 2 sup b sup . The min entropy is always less than or equal to the Shannon entropy it is equal when all the probabilities p sub i sub are equal. Min entropy is important in the theory of randomness extractor . The notation math H infty X math derives from a parameterized family of Shannon like entropy measures, R nyi entropy , math H k X log sqrt k 1 begin matrix sum i p i k end matrix math k 1 is the Shannon entropy. As k is increased, more weight is given to the larger probabilities, and in the limit as k , only the largest p i has any effect on the result. See also R nyi entropy Leftover hash lemma , Extractor References unreferenced date July 2008 Category Entropy and information Category Information theory probability stub ... more details
In statistical mechanics , configuration entropy is the portion of a system s entropy that is related to the position of its constituent particles rather than to their velocity or momentum . It is physically related to the number of ways of arranging all the particle s of the system while maintaining some overall set of specified system properties, such as energy . The configurational entropy is also known as microscopic entropy or conformational entropy in the study of macromolecules . In general, configurational entropy is the foundation of statistical thermodynamics. ref http www.entropysite.com calpoly talk.html ref It can be shown ref name Young cite book last Young first Hugh coauthors ... of configuration entropy of thermodynamic systems e.g., ideal gas, and other systems ... of the macroscopic entropy defined as dS Q T , where Q is the heat exchanged between the system and the surrounding media, and T is temperature. Therefore configuration entropy is the same as macroscopic entropy. Calculation The configurational entropy is related to the number of possible configurations by Boltzmann s entropy formula math S k B , ln W, math where k sub B sub is the Boltzmann ... can be in states n with probabilities P sub n sub , the configurational entropy of the system ... 1 , the entropy vanishes. This formulation is analogous to that of Entropy information theory Shannon s information entropy . The mathematical field of combinatorics , and in particular the mathematics of combination s and permutation s is highly important in the calculation of configurational entropy ..., but also analytically to determine the configurational entropy is the Widom insertion method . See also Conformational entropy Combinatorics Entropic force Nanomechanics Entropy of mixing Notes references ... Category Thermodynamic entropy Category Philosophy of thermal and statistical physics Category Fundamental physics concepts Entropy it Entropia configurazionale ... more details
Citations missing date April 2007 Entropy monitoring is a relatively new method of assessing anaesthetic depth. It was commercially developed by Datex Ohmeda, now part of GE Healthcare . It relies on a method of assessing the degree of irregularity in electroencephalogram EEG signals. The founding principle behind this theory is that the irregularity within an EEG signal decreases with increasing brain levels of anaesthetic drugs. If we relate the irregularity to the Information entropyentropy within the signal, then an entropy scale can be assigned. The signal is captured via a forehead mounted sensor, in a similar way employed by bispectral index BIS . Entropy monitors produce two numbers RE Response Entropy, SE State Entropy that are related to frequency bandpass used. Response Entropy incorporates higher frequency components that include that of electromyogram activity. The reason for using higher frequency bandpass in response entropy is to allow faster response from the monitor in relation to clinical state. Published studies show that entropy scores do relate to clinical levels of anaesthetic depth. Most anaesthetic drugs are detectable by entropy monitoring, a notable exception being nitrous oxide , in common with BIS monitoring. Future studies may show reduced levels of intraoperative awareness when using this type of monitoring. Future studies may also look into possibilities of influence on outcome when using depth of anaesthesia monitoring. Other Vital signs such as pulse , heart rate , blood pressure , and movement are indirect indicators of consciousness, and when these are combined with expired gas analysis of inhalational anaesthetic agents, an experienced anaesthetist can be confident a patient is unconscious and not aware of their surroundings. However ... of BIS Bispectral index or Entropy, are converted to a number expressing the likelihood of awareness. See also bispectral index evoked potentials anaesthesia awareness References Bein B Entropy ... more details
Unreferenced date December 2009 Infobox Album See Wikipedia WikiProject Albums Name Entropy Type ep Artist Anathallo , Javelins Cover anathallo javelins split.jpg Released 2005 Genre Indie rock Label Potential Getaway Driver Last album Hymns EP br 2004 This album Entropy Split One Sided 12 with Javelins br 2005 Next album Floating World Anathallo album Floating World br 2006 Entropy is a split vinyl record vinyl album by Anathallo and Javelins . Each band has one song featured on the album, released in 2005 on Potential Getaway Driver . There were two pressings made, 300 in translucent green and later another 500 in clear vinyl. Track listing Entropy by Javelins Entropy by Anathallo DEFAULTSORT Entropy Album Category Split EPs Category 2005 EPs 2000s indie rock album stub ... more details
Unreferenced date December 2009 In information theory , the cross entropy between two probability distribution s measures the average number of bit s needed to identify an event from a set of possibilities ... the true distribution math p math . The cross entropy for two distributions math p math and math q ... mathrm H p D mathrm KL p q math , where math mathrm H p math is the information entropyentropy of math ... p math also known as the relative entropy . For discrete random variable discrete math p math and math ... math mathrm H p,q math is sometimes used for both the cross entropy as well as the joint entropy of math p math and math q math . Estimation There are many situations where cross entropy needs to be measured ... a model is created based on a training set math T math , and then its cross entropy is measured on a test ... by the model. Since the true distribution is unknown, cross entropy cannot be directly calculated. In these cases, an estimate of cross entropy is calculated using the following formula math ... that the sum is calculated over math N math . This is a Monte Carlo estimate of the true cross entropy, where the training set is treated as samples from math p x math . Cross entropy minimization Cross entropy minimization is frequently used in optimization and rare event probability estimation see the cross entropy method . When comparing a distribution math q math against a fixed reference distribution math p math , cross entropy and Kullback Leibler divergence KL divergence are identical up ... math , which is math 0 math for KL divergence, and math mathrm H p math for cross entropy. In the engineering ... is often called the Principle of Minimum Cross Entropy MCE , or Minxent . However, as discussed in the article ..., with some authors attempting to resolve the inconsistency by redefining cross entropy to be D sub KL sub p q , rather than H p , q . See also Cross entropy method conditional entropy DEFAULTSORT Cross Entropy Category Entropy and information de Kreuzentropie es Entrop a cruzada fr Entropie ... more details
The entropy of activation is one of the two parameters typically obtained from the temperature dependence of a reaction rate, when these data are analysed using the Eyring equation . Symbolized S sup sup , the entropy of activation provides clues about the molecularity of the rate determining step in a reaction, i.e. whether the reactants are bonded to each other, or not. Positive values suggest that entropy increases upon achieving the transition state, which often indicates a Dissociative substitution dissociative mechanism . Negative values for S sup sup indicate that entropy decreases upon achieving the transition state, which often indicates an Associative substitution associative mechanism . Values near zero are difficult to interpret. ref J. H. Espenson Chemical Kinetics and Reaction Mechanism McGraw Hill, 1981, ISBN 0 070019667 2. ref References references Category Chemical kinetics ... more details
Conformational entropy is the entropy associated with the physical arrangement of a polymer chain that assumes a compact or globular protein globular state in solution. The concept is most commonly applied to biological macromolecule s such as protein s and RNA , but can also be used for polysaccharide s and other polymeric organic compound s. To calculate the conformational entropy, the possible conformations assumed by the polymer may first be discretization discretized into a finite number of states, usually characterized by unique combinations of certain structural parameters, each of which has been assigned an energy level. In proteins, backbone dihedral angle s and side chain rotamer s are commonly used as descriptors, and in RNA the base pair ing pattern is used. These characteristics ... mechanics sense of a possible microstate . The conformational entropy associated with a particular .... The entropy of heterogeneous random coil or denaturation biochemistry denatured proteins is significantly ... entropy of the amino acid side chain s in a protein is thought to be a major contributor to the energetic ... Doig Doig AJ, Sternberg MJE. 1995 . Side chain conformational entropy in protein folding. Protein Science 4 2247 51. ref However, a recent study has shown that side chain conformational entropy can ... On Side Chain Conformational Entropy of Proteins. PLoS Comput Biol 2 12 e168. doi 10.1371 journal.pcbi.0020168 ref The conformational entropy of RNA and proteins can be estimated for example, empirical methods to estimate the loss of conformational entropy in a particular side chain on incorporation ... of side chain conformational entropy in protein folding. J Mol Biol 231 3 825 39. ref math S R Sigma ... lowers the conformational entropy of the denatured state and thus increases the energy difference ... 83 1994 . ref References reflist See also Configuration entropy Folding funnel Molten globule Loop entropy Protein folding biochem stub Category Protein structure Category Thermodynamic entropy ... more details
Superherobox image caption character name Entropy alter ego Mr. No One. species Cosmic entities Marvel Comics Cosmic entity publisher Marvel Comics debut creators Peter David br ChrisCross alliances aliases Mr. No One. powers List of comic book superpowers Omnipotence Nigh Omnipotence br br Virtually Unlimited Ability to manipulate, create, or destroy all Matter and Energy at will. br br Omniscience As an abstract concept of the universe . Entropy is a Cosmic entities Marvel Comics Cosmic Entity in the Marvel Comics Marvel Universe Universe who possesses List of comic book superpowers Omnipotence Nigh Omnipotence . A representation of Eternity formed at the beginning of time , whose purpose is to undo, so the cycle of creation and destruction will forever continue. Primarily associated with Genis ... Birth Of EntropyEntropy was created at the beginning of time, possibly when Eternity comics Eternity was formed, Entropy came into being with the seven friendless. Just as all the other friendless have purposes of their own, Entropy s purpose is to destroy, juxtaposed to his father, Eternity, whose purpose entails creation. Entropy and Captain Marvel Entropy and his sister, Epiphany, engineered ... Doon to help him ascertain the cause of his friend s insanity. To prevent Rick from interfering Entropy killed Shinga Doon before he could answer Rick s question. ref Captain Marvel vol 5 2 ref Entropy later meets Genis, revealing he was the son of Eternity comics Eternity . Entropy seeks to destroy ... a paradox resulting in Entropy becoming a new Eternity. The universe is recreated, albeit ... of one of the strongest forces in existence, Entropy has unlimited ability to manipulate space, time, energy and matter on a cosmic scale. Appearance As an abstract concept of the universe, Entropy has no physical form, but Entropy s appearance can vary from lifeform to lifeform, it appears in whatever form that species could perceive him as. References Reflist Marvel Cosmic DEFAULTSORT Entropy ... more details
Unreferenced stub auto yes date December 2009 The entropy of fusion is the increase in entropy when melting a substance. This is almost always positive since the EntropyEntropy as a measure of disorder degree of disorder increases in the phase transition transition from an organized crystal line solid to the disorganized structure of a liquid the only known exception is helium . sfn Atkins Jones 2008 p 236 It is denoted as S sub fus sub and normally expressed in Joule J mole unit mol Kelvin K A natural process such as a phase change will occur when the associated change in the Gibbs free energy is negative. It follows that the entropy of fusion is related to the melting point and the heat of fusion math Delta H fus T fus times Delta S fus math Helium 3 has a negative entropy of fusion at temperatures below 0.3 K. Helium 4 also has a very slightly negative entropy of fusion below 0.8 K. This means that, at appropriate constant pressures, these substances freeze with the addition of heat. sfn Ott Boerio Goates 2000 pp 92 93 Notes Reflist References Citation last Atkins first Peter last2 Jones first2 Loretta year 2008 title Chemical Principles The Quest for Insight edition 4th publisher W. H. Freeman and Company isbn 0 7167 7355 4 page 236 Citation last Ott first J. Bevan last2 Boerio Goates first2 Juliana year 2000 title Chemical Thermodynamics Advanced Applications publisher Academic Press isbn 0 12 530985 6 See also Entropy of vaporization DEFAULTSORT Entropy Of Fusion Category Thermodynamic entropy Category Thermodynamic properties Chem stub ar de Schmelzentropie it Entropia di fusione sv Sm ltentropi ... more details
Expert subject Physics date June 2009 Context date June 2009 In quantum mechanics , and especially quantum information quantum information theory , the linear entropy of a quantum state state is a scalar physics scalar defined as math S L , dot , 1 mbox Tr rho 2 , math where math rho , math is the density matrix of the state. The linear entropy can range between zero, corresponding to a completely pure state, and math 1 1 d , math , corresponding to a completely mixed state. Here, math d , math is the dimension of the density matrix. Linear entropy is trivially related to the purity quantum mechanics purity math gamma , math of a state by math S L , , 1 gamma , . math Motivation The linear entropy is an approximation to the Von Neumann entropy math S , math , which is defined as math S , dot , mbox Tr rho log 2 rho , . math The linear entropy is obtained by approximating math ln rho , math with the first order term math rho 1 , math in the Mercator series math mbox Tr rho log 2 rho , to mbox Tr rho rho 1 mbox Tr rho rho 2 1 mbox Tr rho 2 S L math where the unit trace property of the density matrix has been used to get the second to last equality. The linear entropy and Von Neumann entropy are similar measures of the mixedness of a state, although the linear entropy is easier to calculate because it does not require the Diagonalizable matrix diagonalization of the density matrix. Alternate definition Some authors ref cite journal author Nicholas A. Peters, Tzu Chieh Wei, Paul G. Kwiat title Mixed state sensitivity of several quantum information benchmarks year 2004 journal Physical Review A volume 70 pages 052309 doi 10.1103 PhysRevA.70.052309 arxiv quant ph 0407172 bibcode 2004PhRvA..70e2309P issue 5 ref define linear entropy with a different normalization math S L , dot , frac d d 1 1 mbox Tr rho 2 , . math This ensures that the quantity ranges from zero to unity. References references Category Quantum mechanics quantum stub ... more details
Infobox album See Wikipedia WikiProject Albums Name Port Entropy Type studio Artist Shugo Tokumaru Cover Released April 21, 2010 Recorded 2009 Genre Indie Pop Length 37 24 Label P Vine Japan Polyvinyl Records Polyvinyl U.S. Producer Shugo Tokumaru No reviews in the infobox, please read Template Infobox album Allmusic Rating 4 5 Allmusic class album id port entropy r2047096 pure url yes link Clash magazine Clash rating 6 10 http www.clashmusic.com reviews shugo tokumaru port entropy link One Thirty BPM 70 http onethirtybpm.com 2010 06 21 album review shugo tokumaru port entropy link Pitchfork Media 6.2 10 http pitchfork.com reviews albums 14792 port entropy link The Skinny magazine The Skinny rating 4 5 http www.theskinny.co.uk article 100774 shugo tokumaru port entropy link sputnikmusic rating 4 5 http www.sputnikmusic.com review 38401 Shugo Tokumaru Port Entropy link Last album Exit Shugo Tokumaru album Exit br 2007 This album Port Entropy br 2010 Port Entropy is the fourth studio album from Japanese multi instrumentalist Shugo Tokumaru . It was released on April 21, 2010 on P Vine Records to generally positive reviews. Track listing Platform 0 44 Tracking Elevator 3 20 Linne 3 51 Lahaha 3 11 Rum Hee 3 46 Laminate 3 59 River Low 2 18 Straw 2 37 Drive thru 3 28 Suisha 3 16 Orange 4 11 Malerina 2 43 External links http www.shugotokumaru.com Shugo Tokumaru http www.polyvinylrecords.com store index.php?id 1553 Port Entropy on Polyvinyl website Category 2010 albums Category Shugo Tokumaru albums Category P Vine Records albums ... more details
Expert subject Cryptography date February 2009 In computing , entropy is the randomness collected by an operating ... or specially provided randomness generators. Entropy in the Linux kernel The Linux kernel generates entropy from Keyboard computing keyboard timings, Mouse computing mouse movements, and Integrated ... Linux kernel patches allowing one to use more entropy sources. ref http www.robot101.net 2005 09 25 missing entropy Robotic Tendencies Missing entropy Bot generated title ref The audio entropyd ... , allows audio data to be used as an entropy source. ref https admin.fedoraproject.org pkgdb packages ... is to use the HAVEGE algorithm through haveged to pool entropy. ref cite web title haveged A simple entropy daemon url http www.issihosts.com haveged accessdate 3 April 2011 ref In some systems, network interrupts can be used as an entropy source as well. ref https linuxlink.timesys.com docs about entropyEntropy and Random Devices LinuxLink by TimeSys Your Embedded Linux Resource Bot generated ... depletes dev random whenever it is being read. ref http www.av8n.com turbid paper turbid.htm High Entropy Randomness Generator Bot generated title ref Entropy in the Hurd kernel A driver ported from the Linux kernel has been made available for the Hurd kernel. ref http ibofobi.dk stuff hurd entropy dev ,u random driver for GNU Hurd ibofobi.dk ref Entropy in Solaris dev random and dev urandom have ... 7d?a view Solaris dev random ref As of Solaris 10, administrators can remove existing entropy ... Entropy in OS 2 There is a software package for OS 2 that allows software processes to retrieve random data. ref http r6.ca RexxEGD Rexx Entropy Gathering Daemon for OS 2 ref Entropy in Windows Microsoft Windows releases newer than 95A feature the CryptoAPI CAPI API that gathers entropy in a similar ... RNG Seed to store a seeded value from all of its entropy sources. ref http www.mail archive.com openssl dev openssl.org msg21829.html Source for entropy on Windows platforms with CryptoAPI installed ... more details
Thermodynamics cTopic List of thermodynamic properties System properties Introductory article EntropyEntropy is a measure of how evenly energy is distributed in a system. In a physical system, entropy ... heat flows from a hot region to a cold region, entropy increases as heat is distributed throughout the system. The concept of entropy is central to the second law of thermodynamics . The second law ... as saying that the entropy of an isolated system always increases, and processes which increase entropy can occur spontaneously. Since entropy increases as uniformity increases, the second law says qualitatively that uniformity increases. The term entropy was coined in 1865 by the German physicist ... Cite web title etymonline.com entropy url http www.etymonline.com index.php?search entropy&searchmode none accessdate 2009 06 15 ref Explanation The concept of thermodynamic entropy arises from the second law of thermodynamics . It uses entropy to quantify the capacity of a system for change, namely ... whether a thermodynamic process may occur. Entropy is defined by two descriptions, first as a macroscopic ... ed., Wiley 2008 , p. 125 ref math rm d S frac rm delta q T . math Where d S is the change in entropy ... of entropy does not allow the determination of an absolute value, only of differences. The second definition of entropy comes from statistical mechanics . The entropy of a particular Microstate statistical ... B ln Omega, math Where S is the entropy, k sub B sub is the Boltzmann constant, and &Omega is the number ... will result in a decrease in the internal energy of the thermodynamic system . Thermodynamic entropy ... to becoming dispersed or spread out, if it is not hindered from doing so. Entropy change is the quantitative ... it has become spread out at a specific temperature. Entropy has been developed to describe any of several phenomena, depending on the field and the context in which it is being used. Information entropy ... unconnected with heat and energy. Image Ice water.jpg thumb Ice melting provides an example of entropy ... more details
The volume entropy is an asymptotic invariant mathematics invariant of a compact space compact Riemannian manifold that measures the exponential growth rate of the volume of metric ball s in its universal cover . This concept is closely related with other notions of entropy found in dynamical systems and plays an important role in differential geometry and geometric group theory . If the manifold is nonpositively curved then its volume entropy coincides with the topological entropy of the geodesic flow . It is of considerable interest in differential geometry to find the Riemannian metric on a given smooth manifold which minimizes the volume entropy, with locally symmetric space s forming a basic class of examples. Definition Let M , g be a compact Riemannian manifold, with universal cover math tilde M . math Choose a point math tilde x 0 in tilde M math . The volume entropy or asymptotic volume growth math h h M, g math is defined as the limit math h M,g lim R rightarrow infty frac log ... of balls in the universal cover as a function of the radius. Properties Volume entropy h is always bounded above by the topological entropy h sub top sub of the geodesic flow on M . Moreover .... More generally, volume entropy equals topological entropy under a weaker assumption that M is a closed ... entropy when the volume is prescribed. This is a corollary of a very general result due to Besson ... in differential geometry of surfaces Katok s entropy inequality was recently exploited to obtain a tight ... localement sym triques de courbure strictement n gative. French Entropy and rigidity of locally symmetric spaces with strictly negative curvature Geom. Funct. Anal. 5 1995 , no. 5, 731 799 Katok, A. Entropy ... Katz, M. Sabourau, S. Entropy of systolically extremal surfaces and asymptotic bounds. Erg. Th. Dyn. Sys. 25 2005 , 1209 1220 Manning, A. Topological entropy for geodesic flows. Ann. of Math. 2 110 1979 , no. 3, 567 573 Category Differential geometry Category Dynamical systems Category Entropy Category ... more details
Image Entropy mutual information relative entropy relation diagram.svg thumb 256px right Individual H X ,H Y , joint H X,Y , and conditional entropies for a pair of correlated subsystems X,Y with mutual information I X Y . Joint entropy information theory entropy is a measure of the uncertainty associated with a set of random variables variables . Definition The joint entropy of two variables math X math and math Y math is defined as math H X,Y sum x sum y P x,y log 2 P x,y math where math x math and math y math are particular values of math X math and math Y math , respectively, math P x,y math is the probability of these values occurring together, and math P x,y log 2 P x,y math is defined to be 0 if math P x,y 0 math . For more than two variables math X 1, ..., X n math this expands to math H X 1, ..., X n sum x 1 ... sum x n P x 1, ..., x n log 2 P x 1, ..., x n math where math x 1,...,x n math are particular values of math X 1,...,X n math , respectively, math P x 1, ..., x n math is the probability of these values occurring together, and math P x 1, ..., x n log 2 P x 1, ..., x n math is defined to be 0 if math P x 1, ..., x n 0 math . Properties Greater than individual entropies The joint entropy of a set of variables is greater than or equal to all of the individual entropies of the variables in the set. math H X,Y geq max H X ,H Y math math H X 1, ..., X n geq max H X 1 , ..., H X n math Less than sum of individual entropies The joint entropy of a set of variables is less than or equal to the sum of the individual entropies of the variables in the set. This is an example of subadditivity . This inequality is an equality if and only if math X math and math Y math are statistically independent . math H X,Y leq H X H Y math math H X 1, ..., X n leq H X 1 ... H X n math Relations to Other Entropy Measures Joint entropy is used in the definition of conditional entropy ... theory , the joint entropy is generalized into the joint quantum entropy . Category Entropy ... more details
In information theory an entropy encoding is a lossless data compression scheme that is independent of the specific characteristics of the medium. One of the main types of entropy coding creates and assigns a unique prefix free code to each unique symbol that occurs in the input. These entropy information theory entropy encoders then compress data by replacing each fixed length input symbol by the corresponding variable length prefix free output codeword. The length of each codeword is approximately Proportionality mathematics proportional to the negative logarithm of the probability . Therefore, the most common symbols use the shortest codes. According to Claude Shannon Shannon s source coding theorem , the optimal code length for a symbol is &minus log sub b sub P , where b is the number of symbols used to make output codes and P is the probability of the input symbol. Two of the most common entropy encoding techniques are Huffman coding and arithmetic coding . If the approximate entropy characteristics of a data stream are known in advance especially for signal compression , a simpler static code may be useful. These static codes include Universal code data compression universal codes such as Elias gamma coding or Fibonacci coding and Golomb coding Golomb codes such as unary coding or Rice coding . Entropy as a measure of similarity Besides using entropy encoding as a way to compress digital data, an entropy encoder can also be used to measure the amount of similarity between streams of data. This is done by generating an entropy coder compressor for each class of data unknown data is then classified by feeding the uncompressed data to each compressor and seeing which compressor yields the highest compression. The coder with the best compression is probably the coder trained on the data that was most similar to the unknown data. See also Entropy information theory External ... Compression Methods Category Lossless compression algorithms Category Entropy and information ... more details
About entropy in geometry and topology other uses Entropy disambiguation In mathematics , the topological entropy of a topological dynamical system is a nonnegative real number that measures the complexity of the system. Topological entropy was first introduced in 1965 by Adler, Konheim and McAndrew. Their definition was modelled after the definition of the Kolmogorov Sinai entropy Kolmogorov Sinai , or metric, entropy. Later, Dinaburg and Rufus Bowen gave a different, equivalent definition reminiscent of the Hausdorff dimension . The second definition clarified the meaning of the topological entropy for a system given by an iterated function , the topological entropy represents the exponential growth rate of the number of distinguishable orbits of the iterates. An important variational principle relates the notions of topological and measure theoretic entropy. Definition A topological dynamical ... and a continuous function topology continuous self map f . Its topological entropy is a nonnegative ... . The use of arbitrary covers yields the same value of entropy. ref For two covers C and D , let math ... ldots vee f n 1 C . math Then the topological entropy of f , denoted h f , is defined to be the supremum ... by the partition C . Thus the topological entropy is the average per iteration amount of information ... the maximum cardinality of an n , &epsilon separated set. The topological entropy of the map f is defined ... dynamical system X , f . Rufus Bowen extended this definition of topological entropy ... For the measure of correlations in systems with topological order see Topological entanglement entropy ... 9947 196502 114 3A2 3C309 3ATE 3E2.0.CO 3B2 N Topological Entropy , Transactions of the American ... Adler, Tomasz Downarowicz, Micha Misiurewicz, http www.scholarpedia.org article Topological entropy Topological entropy at Scholarpedia PlanetMath attribution id 6068 title Topological Entropy Category Entropy and information Category Ergodic theory Category Topological dynamics fr Entropie topologique ... more details
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