About entropy in thermodynamics entropy in information theory Entropy information theory other uses Entropy disambiguation Seeintro 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 In complex systems of molecules ... water mixture, entropy can either increase or decrease depending on system parameters, such as temperature ... place under adiabatic conditions the entropy of the resulting crystal will be greater than that of the supercooled ..., however, when ice melts, the entropy of the two adjoined systems, the hot and cold bodies, increases. Here are some further tutorials http jchemed.chem.wisc.edu JCESoft 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 as an increase in the disgregation ... Entropy is a thermodynamics thermodynamic property that is a measure of the energy not available ... maximum efficiency when converting energy to work. During this work entropy accumulates in the system, but has to be removed by dissipation in the form of waste heat. The concept of entropy is defined by the second law of thermodynamics , which states that the entropy of a closed system thermodynamics closed system always increases or remains constant. Thus, entropy is also a measure ... the state of order of the initial systems, and therefore entropy is an expression of disorder or randomness. This model is the basis of the microscopic interpretation of entropy in statistical mechanics ... quantum state quantum mechanical states , a model directly related to the information entropy . Thermodynamic entropy has the dimension of energy divided by temperature , and a unit of joule s per kelvin J K in the International System of Units . The term entropy was coined in 1865 by Rudolf Clausius ... 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 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 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 , a Riemannian invariant measuring the exponential rate of volume growth of a Riemannian metric Computer science Entropy anonymous data store , a computer ... more details
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 laws, instead of the traditional exponentials. See also Tsallis entropy Statistical mechanics topics Category Probability theory Category Entropy and information Category Thermodynamic entropy Category Information theory condensedmatter stub ... more details
Unreferenced stub auto yes date December 2009 The entropy of fusion is the increase in entropy when melting 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 to the disorganized structure of a liquid . 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 See also Entropy of vaporization DEFAULTSORT Entropy Of Fusion Category Thermodynamic entropy Category Thermodynamic properties Chem stub de Schmelzentropie it Entropia di fusione sv Sm ltentropi ... 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 . 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 standard entropy change of vaporization is related to the boiling point and the standard enthalpy change 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 de Verdampfungsentropie it Entropia di vaporizzazione ... 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 Category Thermodynamic entropy Category Statistical mechanics thermodynamics stub ... more details
Citations missing date April 2007 Mergeto Entropy anesthesiology date March 2008 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 ..., synchronicity, and burst suppression , that, in the case of BIS Bispectral index or Entropy, are converted ... anaesthesia awareness References Bein B Entropy Best practice&research clinical anesthesiology.Vol ... 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 Roger Freedman year 2008 title University Physics edition 12th Ed. publisher Pearson Education ref that the variation of configuration entropy of thermodynamic systems e.g., ideal gas, and other systems with a vast number of internal degrees of freedom in thermodynamic process es is equivalent to the variation 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 ... of configurational entropy. In particular, this field of mathematics offers formalized ... most often in computer simulations, 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 References cite book last Kroemer first Herbert coauthors ... Category Statistical mechanics Category Thermodynamic entropy Category Philosophy of thermal and statistical physics Category Fundamental physics concepts Entropy it Entropia configurazionale ... 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 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
Orphan date January 2011 Infobox Journal title Entropy cover Image entropy journal logo.gif discipline Physics , Chemistry , Biology , Engineering , Computer sciences , Economics , Philosophy language English abbreviation Sensors publisher MDPI country Switzerland frequency Quarterly history 1999 openaccess Yes website http www.mdpi.com journal entropy ISSN 1099 4300 Entropy ISSN 1099 4300 , an International and Interdisciplinary Journal of Entropy and Information Studies, is published by MDPI in Basel , Switzerland , and is a peer reviewed Open access publishing Open Access journal. External links http www.mdpi.org Molecular Diversity Preservation Int. MDPI Category Engineering journals Category Physics journals Category Chemistry journals Category Open access journals Category Molecular Diversity Preservation International academic journals fr Entropy journal ... more details
In physics, the Tsallis entropy is a generalization of the standard Entropy statistical thermodynamics Boltzmann Gibbs entropy . In the scientific literature is highly debated the physical relevance of the Tsallis entropy. It is in fact not clear if any system obeys, and in this case in which regime, to the statistical mechanics that can be derived from such approach. The Tsallis entropy is defined as math S q p 1 over q 1 left 1 int p x q , dx right , math or in the discrete case math S q p 1 over q 1 left 1 sum x p x q right , math where S denotes entropy, p the probability distribution of interest, and q is a real parameter. In the limit as q &rarr 1, the normal Boltzmann Gibbs entropy is recovered. The parameter q is a measure of the non extensive quantity extensitivity of the system of interest. There are continuous and discrete versions of this entropic measure. Various relationships The discrete Tsallis entropy satisfies math S q left D q sum i p i x right x 1 math where D sub q sub is the q derivative . Non additivity Given two independent systems A and B , for which the joint probability density function probability density satisfies math p A, B p A p B , , math the Tsallis entropy of this system satisfies math S q A,B S q A S q B 1 q S q A S q B . , math From this result, it is evident that the parameter math 1 q math is a measure of the departure from additivity. In the limit when q 1, math S A,B S A S B , , math which is what is expected for an additive system. See also R nyi entropy References Unreferenced date March 2011 External links http www.cscs.umich.edu crshalizi notabene tsallis.html Tsallis Statistics, Statistical Mechanics for Non extensive Systems and Long Range Interactions condensedmatter stub Category Probability theory Category Entropy and information Category Thermodynamic entropy Category Information theory Category Q analogs pt Entropia de Tsallis ... 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
Entropy, from Captain Marvel vol. 1 2 of Captain Marvel v2 1. br Art by Peter David . character name Entropy alter ego Mr. No One. species Cosmic entities Cosmic entity publisher Marvel Comics debut ... all Matter and Energy at will. br br Omniscience As an abstract concept of the universe . Entropy ... Biography 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 engineered the insanity ... to help him ascertain the cause of his friend s insanity. Possibly knowing this, Entropy killed Shinga Doon before he could answer Rick s question, crushing him with an invisible force. Entropy then spoke ... hear the voice of Epiphany, Entropy s sister, conversing with Entropy himself. Rick then went to confront Entropy, at the time not knowing who he was. At the same time, Captain Marvel tried to kill himself, sending Rick into unconsciousness due to their symbiotic relationship. Entropy ... his father. Entropy then went on to reveal his true purpose and nature that he was the offspring ... drove him insane. Marvel gladly accepted. Marvel and Entropy, along with Rick and Epiphany, stood in nothingness ... , and this sparked an argument between himself and Rick. To prove his point, Marvel asked Entropy whether or not he was God, but Entropy could not answer, because he had accomplished his purpose. Rick suggested that next Entropy should do what he knew, and that was what his father s purpose was to create. Creating something was the first new concept Entropy ever had and decided to do it. However, he ... Entropy knew was what his father was, so he created a Big Bang, recreating the universe and becoming ..., Entropy has unlimited ability to manipulate space, time, energy and matter on a cosmic scale. Appearance ... 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 eo Vikipedio Projekto matematiko Minimum entropio ... 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 archive quant ph id 0407172 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
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 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 ... must be integral integrated over the temperature path. This definition 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 mechanics macrostate ... S is the entropy, k sub B sub is the Boltzmann constant, and &Omega is the number of microstates ... in the internal energy of the thermodynamic system . Thermodynamic entropy provides a comparative ... or spread out, if it is not hindered from doing so. Entropy change is the quantitative measure ... 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 takes the mathematical ... more details
Unreferenced date December 2009 Mergeto Shannon index date March 2008 Ecological entropy is a measure of biodiversity in the study of biological ecology . Definition Assume that within a system of unlimited individuals, there exists math n math species of organism s math A 1, A 2, ..., A j, ..., A n math , and the probability that an individual belongs to species math A j math is math p j math , where math sum i 1 n p i 1 math If there are math q math individuals for each species, the population will be math q 1 q 2 ... q j ... q n math . The number of individuals is math q n 10 n log q math . Set math N math as constant math C math . Diversity within each species, such as male, female, large, small, etc. can be expressed as math C sum j p i log q j C sum j p i log p I C log q quad mbox since q j qp I math Hence the specific diversity can be derived by subtracting the diversities within the species from the diversity of the whole population math C log q C sum j p i log p i C log q C sum j p i log p i math The expression is the same as that of information entropy, except that it is customary to use binary logarithm base 2 for information entropy, the unit being bit , and to use common logarithm base 10 for ecological entropy, the unit being decibel bel . The thermodynamic entropy uses natural logarithm base math e math , so that the constant math C math becomes the Boltzmann constant , the ratio of universal gas constant and Avogadro s number . See also Entropy thermodynamics Entropy information theory DEFAULTSORT Entropy Ecology Category Measurement of biodiversity Category Entropy and information zh ... 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
In the mathematical theory of probability , the entropy rate or source information rate of a stochastic process is, informally, the time density of the average information in a stochastic process. For stochastic processes with a countable index, the entropy rate H X is the limit of the joint entropy of n members of the process X sub k sub divided by n , as n Limit mathematics tends to infinity math H X lim n to infty frac 1 n H X 1, X 2, dots X n math when the limit exists. An alternative, related quantity is math H X lim n to infty H X n X n 1 , X n 2 , dots X 1 math For strongly stationary stochastic processes, math H X H X math . Entropy rates for Markov chains Since a stochastic process defined by a Markov chain that is irreducible and aperiodic has a stationary distribution , the entropy rate is independent of the initial distribution. For example, for such a Markov chain Y sub k sub defined on a countable number of states, given the transition matrix P sub ij sub , H Y is given by math displaystyle H Y sum ij mu i P ij log P ij math where &mu sub i sub is the stationary distribution of the chain. A simple consequence of this definition is that the entropy rate of an independent and identically distributed i.i.d. stochastic process has an entropy rate that is the same as the entropy of any individual member of the process. See also Information source mathematics Markov information source References Cover, T. and Thomas, J. 1991 Elements of Information Theory, John Wiley and Sons, Inc., ISBN 0471062596 http www3.interscience.wiley.com cgi bin bookhome 110438582?CRETRY 1&SRETRY 0 External links http www.eng.ox.ac.uk samp Systems Analysis, Modelling and Prediction SAMP , University of Oxford MATLAB code for estimating information theoretic quantities for stochastic processes. Category Information theory Category Entropy Category Markov models de Entropierate ... 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 ... 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, if a coding scheme is used based on a given probability distribution math q math , rather than the true distribution math p math . The cross entropy for two distributions math p math and math q math over the same probability space is thus defined as follows math mathrm H p, q mathrm E p log q mathrm H p D mathrm KL p q math , where math mathrm H p math is the information entropyentropy of math p math , and math D mathrm KL p q math is the Kullback Leibler divergence of math q math from 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, and then its cross entropy is measured on a test set to assess .... 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 H T,q sum ... is calculated over math N 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 math mathrm H p math for cross entropy. In the engineering literature, the principle ... Cross Entropy MCE , or Minxent . However, as discussed in the article Kullback Leibler divergence ... 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 ... 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. External links http www.inference.phy.cam.ac.uk ... . Compression Methods Category Lossless compression algorithms Category Entropy and information ... more details
Loop entropy is the entropy lost upon bringing together two residues of a polymer within a prescribed distance. For a single loop, the entropy varies logarithmically with the number of residues math N math in the loop math Delta S alpha k B ln N , math where math k B math is Boltzmann s constant and math alpha math is a coefficient that depends on the properties of the polymer. This entropy formula corresponds to a power law distribution math P sim N alpha math for the probability of the residues contacting. The loop entropy may also vary with the position of the contacting residues. Residues near the ends of the polymer are more likely to contact quantitatively, have a lower math alpha math than those in the middle i.e., far from the ends , primarily due to excluded volume effects. Wang Uhlenbeck entropy The loop entropy formula becomes more complicated with multiples loops, but may be determined for a Gaussian polymer using a matrix method developed by Wang and Uhlenbeck. Let there be math M math contacts among the residues, which define math M math loops of the polymers. The Wang Uhlenbeck matrix math mathbf W math is an math M times M math symmetric, real matrix whose elements math W ij math equal the number of common residues between loops math i math and math j math . The entropy of making the specified contacts equals math Delta S alpha k B ln det mathbf W math As an example, consider the entropy lost upon making the contacts between residues 26 and 84 and residues 58 and 110 in a polymer cf. ribonuclease A . The first and second loops have lengths 58 84 26 and 52 110 58 , respectively, and they have 26 84 58 residues in common. The corresponding Wang Uhlenbeck matrix is math mathbf W stackrel mathrm def begin bmatrix 58 && 26 26 && 52 end bmatrix math whose determinant is 2340. Taking the logarithm and multiplying by the constants math alpha k B math gives the entropy ... Thermodynamic entropy Category Polymer physics ... more details
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