Infobox film name Entropy image Entropy film poster.jpg producer Ashok Amritraj director Phil Joanou writer Phil Joanou starring Stephen Dorff br Judith Godr che br Kelly Macdonald br Lauren Holly br Jon Tenney br Frank Vincent br Paul Guilfoyle br Hector Elizondo br Bray Poor br Kathryn Erbe br Shannon Fiedler br Zach Tyler Eisen credited as Zach Tyler br Jim Gaffigan br Dominic Hawksley cinematography Carolyn Chen editing John Galt distributor Warner Bros. released April 15, 1999 U.S. release runtime 104 min. language English Entropy is a 1999 film directed by Phil Joanou , starring Stephen Dorff and featuring the Irish rock band U2 . The film is largely autobiographical, covering his early film career, his relationships including a very short lived marriage and his pet cat. External links imdb title 0156515 Phil Joanou DEFAULTSORT Entropy Film Category 1999 films indie film stub fr Entropy film ... 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
Cleanup date February 2008 A work on software engineering by Ivar Jacobson et al. ref Citation first1 Ivar last1 Jacobson first2 Magnus last2 Christerson first3 Patrik last3 Jonsson first4 Gunnar last4 vergaard title Object Oriented Software Engineering A Use Case Driven Approach publisher ACM Press. Addison Wesley year 1992 isbn 0201544350 pages 69 70 ref describes software entropy as follows The second law of thermodynamics , in principle, states that a closed system s randomness disorder cannot be reduced, it can only remain unchanged or increase. A measure of this disorder is entropy . This law also seems plausible for software system s as a system is modified, its disorder, or entropy, always increases. This is known as software entropy Within software development , there are similar theories see Lehman 1985 ref Citation first1 M.M. last1 Lehman first2 L.A. last2 Belady title Program evolution processes of software change publisher Academic Press Professional, Inc., San Diego, CA year 1985 ref , who suggested a number of laws, of which two were, basically, as follows A computer program that is used will be modified When a program is modified, its complexity will increase, provided that one does not actively work against this. end of quote from Jacobson Andrew Hunt and David Thomas use Fixing Broken Windows as a metaphor for avoiding software entropy in software development. ref Citation first1 Andrew last1 Hunt first2 David last2 Thomas title The Pragmatic Programmer publisher Addison Wesley year 1999 isbn 0 201 61622 X Item 4 of 22 tips is Don t Live with Broken Windows . ref The process of code refactoring can result in stepwise reductions in software entropy. See also Software brittleness Software rot References Reflist http www.webopedia.com TERM s software entropy.htm Definition of software entropy on Webopedia Category Software metrics Category Software quality Category Software maintenance hr Softverska entropija ... more details
Unreferenced date December 2009 Residual entropy is small amount of entropy which is present even after a substance is cooled arbitrarily close to absolute zero . It occurs if a material can exist in many different microscopic states when cooled to absolute zero. This can occur if it has many different ground states with exactly the same zero point energy it can also occur if the ground states have slightly different energies, but the system is prevented from finding and settling into the true lowest energy state. It is seen most often in substances which have very weak tendencies to align into their energetic ground state, and or which are cooled quickly. A common example is the case of carbon monoxide , which has a very small Molecular dipole moment dipole moment . As the carbon monoxide crystal is cooled to absolute zero, few of the carbon monoxide molecules have enough time to align themselves ... microstate statistical mechanics microstates , giving a residual entropy of math S Nk ln 2 math , rather than zero. Another example is any amorphous solid glass . These have residual entropy, because ... a macroscopic system. History One of the first examples of residual entropy was pointed out by Linus ... words, entropy. Thus systems that can take multiple configurations at or near absolute zero are said to have residual entropy. Although water ice was the first material for which residual entropy was proposed ... entropy. Geometrical frustration Geometrically frustrated systems in particular often exhibit residual entropy. An important example is spin ice , which is a geometrically frustrated magnetic material ..., thereby producing the same 2 in, 2 out rule as in water ice, and therefore the same residual entropy ... is that the level of residual entropy can be controlled by the application of an external magnetic ... disorder Proton disorder in ice Geometrical frustration DEFAULTSORT Residual Entropy Category Thermodynamic entropy de Nullpunktsentropie it Entropia residua zh classical zh ... 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. Example In the Human genome , for chromosome 1, which consists of 247 Base pair Length measurements Mbp , there is an entropy rate of 1.82 bits per base pair. 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 ... Entropy Category Markov models de Entropierate es Ratio de entrop a ... more details
The concept of entropy developed in response to the observation that a certain amount of functional energy ... was the concept of entropy . In the early 1850s, Rudolf Clausius set forth the concept of the thermodynamic ... his ideas of lost energy, and coined the term entropy . Since the mid 20th century the concept of entropy ... energy or entropy , i.e. energy lost to dissipation and friction. ref Cite book author ... of usable caloric was a precursory form of the increase in entropy as we now know it. Though formulated in terms of caloric, rather than entropy, this was an early insight into the second law of thermodynamics ... of entropy In his 1854 memoir, Clausius first develops the concepts of interior work , i.e. ... the first ever mathematical formulation of entropy, although at this point in the development ... equivalent of heat which was developing at the time rather than entropy, a term which was to come into use ... In modern terminology, we think of this equivalence value as entropy , symbolized by S . Thus, using the above description, we can calculate the entropy change S for the passage of the quantity of heat ... a body of steam, to the temperature T sub 2 sub as shown below Image Entropy diagram.png ... Q T math Then, the entropy change or equivalence value for this transformation is math Delta S S rm ... value was a precursory formulation of entropy. ref Clausius, Rudolf. 1856 . On the Application ... forms of the concept of entropy. 1865 definition In 1865, Clausius gave irreversible heat loss ... entropy as a corresponding designation for the transformation contents verwandlungsinhalt of a system ref cquote I propose to name the quantity S the entropy of the system, after the Greek word trope , the transformation. I have deliberately chosen the word entropy to be as similar as possible ... did not specify why he chose the symbol S to represent entropy, it is arguable that Clausius chose ..., Ludwig Boltzmann formulated the alternative definition of entropy S defined as math S k rm B ... more details
Cleanup date May 2008 Social entropy is a Macrosociology macrosociological systems theory . It is a measure of the natural decay within a social system . It can refer to the decomposition of social structure or of the disappearance of Distinction social social distinctions . Much of the energy consumed by a social organization is spent to maintain its structure, counteracting social entropy, e.g., through legal institutions, education and even the promotion of television viewing. Anarchy is the maximum state of social entropy. Social Entropy implies the tendency of social networks and society in general to break down over time, moving from cooperation and advancement towards conflict and chaos. Social Entropy and Energy Inputs Modern Western complex societies remain organized by large inputs of energy to mitigate the natural progression of increasing entropy disorder , according to the Second Law of Thermodynamics , a fundamental law of physics. This effectively states that Entropy disorder increases with time. As the system becomes more complex, through access to energy, it becomes more susceptible to changes that may occur if one were to remove this source of energy. Take away the energy inputs largely from fossil fuels and organization corrodes, thus society becomes less cohesive and trends toward anarchy . Energy Return on Energy Invested theories A related economic model is proposed by Thomas Homer Dixon and by Charles Hall in relation to our declining productivity of energy extraction, or Energy Return on Energy Invested or EROEI. This measures the amount of surplus energy ... in food production again. Entropy in the context of a Micro level The typical progression of time continues to see words appended with marginally altered meanings and or contexts. Entropy is now ... of mind To refer to another person s state of mind as One of entropy or, Entropic is to cite ... D. Bailey sociologist Kenneth D. Bailey 1990 . Social Entropy Theory . Albany, New York State University ... more details
In physics, the Tsallis entropy is a generalization of the standard Boltzmann Gibbs entropy. It was introduced in 1988 by Constantino Tsallis ref name tsallis1988 Cite doi 10.1007 BF01016429 ref as a basis for generalizing the standard statistical mechanics. In the scientific literature, the physical relevance of the Tsallis entropy was occasionally debated. However, from the years 2000 on, an increasingly ... confirm the predictions and consequences that are derived from this nonadditive entropy, such as nonextensive ... entropy and associated statistics apply, the following ones can be selected Anomalous diffusion ref ... theorem ref Cite doi 10.1016 S0375 9601 00 00337 6 ref . Sensitivity to initial conditions and entropy ... PhysRevE.69.045202 ref . Probability sets which make the nonadditive Tsallis entropy to be extensive ... math sum i p i 1 math , the Tsallis entropy is defined as math S q p i 1 over q 1 ... . In the limit as math q to 1 math , the usual Boltzmann Gibbs entropy is recovered, namely math S BG S 1 p k sum i p i ln p i . math For continuous probability distributions, we define the entropy ... function . The Tsallis Entropy has been used along with the Principle of maximum entropy to derive the Tsallis distribution . Various relationships The discrete Tsallis entropy satisfies math S q ... be compared to the standard entropy formula math S lim x rightarrow 1 frac d dx sum i p i x ... function probability density satisfies math p A, B p A p B , , math the Tsallis entropy of this system ... distribution belongs to the statistical exponential families. Tsallis entropy for an exponential family .... For multivariate normal, term k is zero, and therefore the Tsallis entropy is in closed form. See also R nyi entropy Tsallis distribution References references Refbegin cite journal last1 Nielsen ... Nielsen and Richard Nock title A closed form expression for the Sharma Mittal entropy of exponential ... Tsallis Category Probability theory Category Entropy and information Category Thermodynamic entropy ... more details
Infobox Book See Wikipedia WikiProject Novels or Wikipedia WikiProject Books name The Entropy Tango title orig translator image Image Entropy tango.jpg 200px image caption Dust jacket from the first edition author Michael Moorcock illustrator cover artist Romaine Slocombe country United Kingdom language English language English series Jerry Cornelius subject genre Literary fiction publisher New English Library release date 1981 in literature 1981 english release date media type Print Hardcover Hardback pages 152 pp isbn 0 450 04886 1 dewey 823 .914 19 congress PR6063.O59 E5 1981 oclc 8021128 preceded by The Lives and Times of Jerry Cornelius followed by The Adventures of Una Persson and Catherine Cornelius in the Twentieth Century The Entropy Tango is a novel by British fantasy and science fiction writer Michael Moorcock ref cite web title The Entropy Tango last first work amazon.ca url http www.amazon.ca dp 0450056635 date accessdate 2007 12 03 ref . It is part of his long running Jerry Cornelius series. Footnotes Reflist References cite web last first authorlink coauthors title Internet Speculative Fiction Database work publisher date url http www.isfdb.org cgi bin pl.cgi?THNTRPTNGX1981 format doi accessdate 2007 12 16 cite web last first authorlink coauthors title Moorcock s Miscellany work publisher date url http www.multiverse.org imagehive v bookcovers books mikebooks tet format doi accessdate 2007 12 16 cite web last Brown first Charles N. authorlink Charles N. Brown coauthors William G. Contento title The Locus Index to Science Fiction 1984 1998 work publisher date url http www.locusmag.com index t41.htm A4888 format doi accessdate 2007 12 16 DEFAULTSORT Entropy Tango, The Category 1981 novels Category Novels by Michael Moorcock 1980s sf novel stub ... more details
Estimating the differential entropy of a system or process, given some observations, is useful in various science engineering applications, such as Independent Component Analysis , ref Dinh Tuan Pham 2004 Fast algorithms for mutual information based independent component analysis. In Signal Processing .... Du, Y. Wang, J. Guo, S. M. Thouin, P.D. 2006 Survey and comparative analysis of entropy and relative entropy thresholding techniques. In Vision, Image and Signal Processing , Volume 153, Issue 6, 837 ... 2004 , Geodesic entropic graphs for dimension and entropy estimation in manifold learning. In Signal .... ref Benesty, J. Yiteng Huang Jingdong Chen 2007 Time Delay Estimation via Minimum Entropy. In Signal ... references Entropy 20estimation.pdf Nonparametric entropy estimation An overview . In International ... T. Sch rmann, Bias analysis in entropy estimation. In J. Phys. A Math. Gen , 37 2004 , pp. L295 ... that the differential entropy, math H X int mathbb X f x log f x ,dx math can be approximated by producing a histogram of the observations, and then finding the discrete entropy math begin matrix H ... method, and then, from the pdf estimate, compute the entropy. A useful pdf estimate method is e.g. Gaussian ... can then be used to calculate the entropy estimate, in a similar way to that given above for the histogram .... However, using analogous methods, some multidimensional entropy estimators have been developed. ref name lm2003 E. G. Learned Miller 2003 A new class of entropy estimators for multi dimensional ... density and entropy estimators for spherically invariant multidimensional data, In Neural Computation ... point in our dataset, we can find the distance to its nearest neighbour . We can in fact estimate the entropy ... Nemenman2003 Ilya Nemenman, Fariel Shafee, William Bialek 2003 Entropy and Inference, Revisited. Advances ... Ruyter 2004 Entropy and information in neural spike trains Progress on the sampling problem. Physical ... distribution . References reflist DEFAULTSORT Entropy Estimation Category Entropy and information ... more details
In thermodynamics the entropy of mixing is the increase in the total entropy of a compound system, when .... The entropy of mixing is entirely accounted for by the diffusive expansion of each material into a final ... transfer of work or heat, to or from the surroundings also there may be a departure of the entropy ... in entropy of mixing. These energy and entropy variables and their temperature dependences provide valuable information about the properties of the materials. On a molecular level, the entropy of mixing ... species, even though they are chemically non reacting. The entropy of mixing provides information about ... concept of randomness is used for statistical mechanical explanation of the entropy of mixing. Mixing ... volumes , and the entropy of mixing math Delta S mix , math is given by math Delta S mix nR x 1 ... moles of component math i , math may explore the combined volume math V , math , which causes an entropy ..., the increase in entropy is due entirely to the irreversible processes of expansion of the two gases ... change, and the entropy of mixing considered here. For an ideal gas mixture or an ideal solution ... is given by the entropy term only math Delta G mix T Delta S mix , math For an ideal solution ... solutions The above equation for the entropy of mixing of ideal gases is valid also for certain ... Equilibrium 3rd ed., Cambridge University Press 1971 p.432 ref The value of the entropy corresponds .... MacMillan 1969 p.263 ref For binary mixtures the entropy of random mixing can be considered ... math and math ln 1 x math are both negative and the entropy of mixing math Delta S mix , math is positive ... increase the entropy of the system. Random mixing therefore always favors miscibility and opposes phase ... entropy of mixing can occur when the attractive interactions between unlike molecules are significantly ... but only with water molecules, so in solution they remain associated to water molecules with loss of entropy. The mixing which occurs below 19 C is due not to entropy but to the enthalpy of formation ... 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 . In information theory , the conditional entropy or equivocation quantifies the remaining information entropyentropy i.e. uncertainty of a random variable math Y math given that the value of another random variable math X math is known. It is referred to as the entropy of math Y math conditional on math X math , and is written math H Y X math . Like other entropies, the conditional entropy is measured in bit s, nat information nat s, or ban information ban s. Definition More precisely, if math H Y X x math is the entropy of the variable math Y math conditional on the variable math X math taking a certain value math x math , then math H Y X math is the result of averaging math H Y X x math over all possible values math x math that math X math may take. Given discrete random variable math X math with support mathematics support math mathcal X math and math Y math with support math mathcal Y math , the conditional entropy of math Y math given math X math is defined as math ... and Y. The last formula above is the Kullback Leibler divergence , also known as relative entropy. Relative entropy is always positive, and vanishes if and only if math p x,y p x math . This is when knowing ... entropy is math H Y X , ,H X,Y H X , . math This is true because math begin align H Y X & sum x in mathcal ... information theory , the conditional entropy is generalized to the conditional quantum entropy ... entropy, math H X Y y math , can be either lesser or greater than math H X Y math , math H ... Berlin year 2001 pages 370 373 isbn 3 540 41633 1 oclc doi See also Entropy information theory Mutual information Conditional quantum entropy Variation of information Entropy power inequality Likelihood function Category Entropy and information Category Information theory bar Bedingte Entropie ... more details
Differential entropy also referred to as continuous entropy is a concept in information theory that extends the idea of Shannon information entropyentropy , a measure of average surprisal of a random ... entropy math h X math or math h f math is defined as math h X int mathbb X f x log f x ,dx math . As with its discrete analog, the units of differential entropy depend on the base of the logarithm ... bases. Related concepts such as joint entropy joint , conditional entropy conditional differential entropy, and Kullback Leibler divergence relative entropy are defined in a similar fashion. One must take care in trying to apply properties of discrete entropy to differential entropy, since ... Uniform 0 , 1 2 has negative differential entropy math int 0 frac 1 2 2 log2 ,dx log2 , math . Thus, differential entropy does not share all properties of discrete entropy. Note that the continuous ... entropy For two densities f and g , math D f g geq 0 math with equality if math f g math ... rule for differential entropy holds as in the discrete case math h X 1, ldots, X n sum i 1 n h X i X 1, ldots, X i 1 leq sum h X i math . Differential entropy is translation invariant, ie, math h X c h X math for a constant c . Differential entropy is in general not invariant under arbitrary ... distribution below . However, differential entropy does not have other desirable properties It is not invariant under change of variables . It can be negative. A modification of differential entropy that addresses this is the relative information entropy , also known as the Kullback Leibler divergence ... in the normal distribution With a normal distribution , differential entropy is maximized for a given variance. The following is a proof that a Gaussian variable has the largest entropy amongst ... an arbitrary Probability density function PDF with the same variance. Since differential entropy is translation ... . When the entropy of g x is at a maximum and the constraint equations, which consist of the normalization ... more details
Infobox Album See Wikipedia WikiProject Albums Name Paradigm in Entropy Type studio Artist Bleed the Sky band Bleed the Sky Cover ParadigmInEntropy.jpg Released April 19, 2005 Recorded Oct 31, 2004 Nov 28, 2004 Spyder Studios, Strongsville , Ohio OH Genre Metalcore br Groove metal Length 40 53 Label Nuclear Blast Records Nuclear Blast Producer Ben Schigel Last album Bleed the Sky EP br 2004 This album Paradigm in Entropy br 2005 Next album Murder the Dance br 2008 Album ratings rev1 Allmusic rev1score Rating 3 5 ref Allmusic class album id r737147 pure url yes Allmusic review ref Automatically generated by DASHBot Paradigm in Entropy is the debut album by the California based metal music metal music group Bleed the Sky band Bleed the Sky . The album was released on April 19, 2005 through Nuclear Blast Records . Track listing Minion 4 11 Killtank 3 37 Paradigm in Entropy 3 34 Skin Un Skin 4 08 Leverage 3 56 The Martyr 5 50 Gated 3 02 God in the Frame 3 57 Division feat. T.J. Frost & Joe Cafarella of STEMM ref http www.fourteeng.net AlbumReviews.html FourteenG Album Reviews 2005 Releases Bot generated title ref 3 26 Borrelia Mass 5 09 References Reflist Category 2005 debut albums Category Nuclear Blast Records albums Category Bleed the Sky albums Category Article Feedback 5 ... more details
Expert subject Mathematics date November 2008 An entropy maximization problem is a convex optimization problem of the form maximize math f 0 vec x sum i 1 n x i log x i math subject to math A vec x leq b, quad mathbf 1 T vec x 1 math where math vec x in mathbb R n math is the optimization variable, math A in mathbb R m times n math and math b in mathbb R m math are problem parameters, and math mathbf 1 math denotes a vector whose components are all 1. See also Principle of maximum entropy External links cite book last Boyd first Stephen coauthors Lieven Vandenberghe title Convex Optimization publisher Cambridge University Press date 2004 pages p. 362 isbn 0521833787 url http www.stanford.edu boyd cvxbook bv cvxbook.pdf accessdate 2008 08 24 Category Mathematical optimization Category Convex optimization mathapplied stub ... more details
In quantum mechanics , and especially quantum information processing , the entropy exchange of a quantum operation math phi , math acting on the density matrix math rho Q , math of a system math Q , math is defined as math S rho, phi equiv S Q ,R S rho QR math where math S rho QR , math is the von Neumann entropy of the system math Q , math and a fictitious Purification of quantum state purifying auxiliary system math R , math after they are operated on by math phi , math . Here, math rho QR QR rangle langle QR quad math , math mathrm Tr R rho QR rho Q quad math , and math rho QR phi rho QR quad math . References Nielsen, Michael A. and Isaac L. Chuang 2000 . Quantum Computation and Quantum Information , Cambridge University Press, ISBN 0 521 63503 9 Category Quantum information science Quantum stub ... more details
In information theory , the R nyi entropy , a generalisation of Shannon entropy , is one of a family ... Alfr d R nyi . The R nyi entropy of order math alpha math is defined for math alpha geq 0 math and math ... of . Higher values of , approaching infinity, give a R nyi entropy which is increasingly ... zero, give a R nyi entropy which increasingly weights all possible events more equally, regardless of their probabilities. The intermediate case 1 gives the Shannon entropy , which has special properties ... in ecology and statistics as diversity indices indices of diversity . The R nyi entropy is also ... XY spin chain model, the R nyi entropy as a function of can be calculated explicitly by virtue ... group . ref cite journal last Its first A. R. coauthors Korepin, V. E. title Generalized entropy ... Its, A.R., Korepin, V.E. title R nyi entropy as a measure of entanglement in quantum spin chain journal ... n log X , , math which is the logarithm of the cardinality of X , sometimes called the Hartley entropy ... H alpha math converges to math H 1 X sum i 1 n p i log p i math which is the Shannon entropy . Collision entropy , sometimes just called R nyi entropy, refers to the case math alpha 2 math , math ... log sup i 1..n p i math and this is called Min entropy , because it is the smallest value of math H ... H infty H 2 2 H infty math . On the other hand the Shannon entropy math H 1 math can be arbitrarily high for a random variable X with fixed min entropy. math H 2 2 H infty math is because math log sum ... of the probabilities. Why &alpha 1 is special The value 1, which gives the Shannon entropy and the Kullback ... cite conference author A. R nyi title On measures of information and entropy booktitle Proceedings ... Nock title A closed form expression for the Sharma Mittal entropy of exponential families ... 8121 45 3 032003 See also Diversity indices Tsallis entropy Generalized entropy index DEFAULTSORT Renyi entropy Category Information theory Category Entropy and information bar R nyi Entropie de R nyi ... more details
Research concerning the relationship between the thermodynamics thermodynamic quantity entropy and the evolution ... law of thermodynamics and the principle of entropy. ref Adams, Henry. 1986 . History of the United ... feeds on negative entropy, or negentropy as it is sometimes called. Recent writings have utilized ..., 1st Baron Kelvin William Thomson , between his newly developed concept of entropy and life. Building ... which exists in plenty in any body in the form of heat, but a struggle for negative entropy , which ... math S int dQ over tau math where math S math entropy math dQ math equals a differential amount of heat ... McCulloch1876 Rp p. 270 Negative entropy Later, building on this premise, in the famous 1944 book ... or maintains its entropy by feeding on negative entropy . ref Cite book last Schr dinger ... remarks on his usage of the term negative entropy quote Let me say first, that if I had been catering ..., which states that the entropy of an isolated system tends to increase, it does not in any way conflict or invalidate this law, because the principle that entropy can only increase or remain constant .... Whenever a system can exchange either heat or matter with its environment, an entropy decrease of that system ... I d look for an entropy reduction, since this must be a general characteristic of life. Citation ... or a reversal of entropy. Gibbs free energy and biological evolution In recent years, the thermodynamic interpretation of evolution in relation to entropy has begun to utilize the concept of the Gibbs free energy , rather than entropy. Citation needed date June 2011 This is because biological ... free energy is a form of the principle of minimum energy , which follows from the entropy maximization ... as heat and entropy. ref Cite book last Lehninger first Albert title Principles of Biochemistry, 2nd ... A date 8 November 2008 volume 464 issue 2099 pages 3055 3070 bibcode 2008RSPSA.464.3055K ref Entropy ... 1984 Ed. Laurie R. Godfrey, p. 85 ref See also Complex systems Dissipative system Entropy ... more details
Orphan date April 2012 Expert subject date April 2012 Entropy is simply defined as the property used to determine the amount of heat not available to do work in a system. This energy is dispelled as wasted heat. Entropy in terms of the Second Law of Thermodynamics is constantly increasing. Entropy can never decrease in a system unless the entropy of the surroundings is increased. The increased entropy must always be less than or equal to the original entropy. That is to say S sub Universe sub S sub System sub S sub Surroundings sub . Entropy and the environment File Carnot heat engine 2.svg 300px thumb right Carnot engine diagram modern where heat flows from a high temperature T sub H sub furnace through the fluid of the working body working substance and into the cold sink T sub C sub , thus forcing the working substance to do mechanical work W on the surroundings, via cycles of contractions and expansions. The Second Law of Thermodynamics may help provide explanation for why there have been increases in Earth s temperatures over the last 250 years, and many professionals are concerned that the entropy increase of the universe is a real threat to the environment. As an engine operates, heat flows from a heat tank of greater temperature to a heat sink of lesser temperature. ref cite book last Moran first Michael title Fundamentals of Engineering Thermodynamics year 2011 publisher John Wiley and Sons, Inc. location Hoboken, NJ pages 235 266 coauthors Howard H. Shapiro, Daisie D. Boettner, Margaret B. Bailey page 242 chapter 5 ref In between these states, the heat flow is turned into useful energy with the help of heat engines. As these engines operate, however, a great deal of heat is lost to the environment due to inefficiencies. In a Carnot Engine , which is the most ... accessdate 14 April 2012 year 2001 ref With the entropy of the environment constantly increasing, however ..., or there could be the heat death of the universe. Sources Reflist Category Thermodynamic entropy ... more details
Introduction The concept of entropy production is very important. It plays a key role in the thermodynamics of irreversible processes ref S.R. de Groot and P. Mazur, Non equilibrium thermodynamics North Holland Publishing Company, Amsterdam London, 1969 ref , but it is also very important for our daily life. The social impact is immense since it affects the performance of thermal machines such as power plants, heat engines, refrigerators, and air conditioners. This aspect is the topic in this Article. First and second law Entropy production is a key element of the second law of thermodynamics for open inhomogeneous systems which reads math frac dS dt frac dot Q T dot S dot S i math with math dot S i geq 0. math Here S is the entropy of the system T is the temperature at which the heat flow math dot Q math enters the system math dot S dot n S m dot m s math represents the entropy flow into the system, due to matter flowing into the system math dot n, dot m math are the molar and mass flow and S sub m sub and s are the molar and specific entropy of the matter, flowing into the system, respectively math dot S i math represents the entropy production rates due to internal processes. It is always ... a math is released at ambient temperature T sub a sub . A power P is produced and the entropy production .... The power P is supplied and math dot S i math is the entropy production rate. The arrows define ... are cyclic machines. In the steady state the internal energy and the entropy of the machines after ... math xi C frac T L T a T L . math Expressions for the rate of entropy production In case of a heat flow math dot Q math from T sub 1 sub to T sub 2 sub the rate of entropy production is given by math ... the entropy production rate is math dot S i kappa frac A L T 1 T 2 2. math In case of a volume flow ... or on p sub 1 sub p sub 2 sub are quadratic. This is typical for expressions of the entropy production rates in general. It guaranties that the entropy production is positive. Homogeneous systems In homogeneous ... more details
Unreferenced date December 2008 Orphan date December 2008 In astrophysics , what is referred to as entropy is actually the adiabatic invariant adiabatic constant derived as follows. Using the first law of thermodynamics for a quasistatic process quasi static , infinitesimal process for a hydrostatics hydrostatic system math dQ dU dW. , math For an ideal gas in this special case, the internal energy , U, is only a function of the temperature T therefore the partial derivative of heat capacity with respect to T is identically the same as the full derivative, yielding through some manipulation math dQ C V dT P ,dV. math Further manipulation using the differential version of the ideal gas law , the previous equation, and assuming constant pressure, one finds math dQ C P dT V ,dP. math For an adiabatic process math dQ 0 , math and recalling math gamma frac C P C V , math , one finds math frac V ,dP C P dT P ,dV C V dT math math frac dP P frac dV V gamma. math One can solve this simple differential equation to find math PV gamma text constant K , math This equation is known as an expression for the adiabatic constant, K, also called the adiabat. From the ideal gas equation one also knows math P frac rho k B T mu m H , math where math k B , math is Boltzmann s constant . Substituting this into the above equation along with math V grams rho , math and math gamma 5 3 , math for an ideal monatomic gas one finds math K frac k B T mu m H rho 2 3 , math where math mu , math is the mean molecular weight of the gas or plasma physics plasma and math m H , math is the mass of the Hydrogen atom , which is extremely close to the mass of the proton , math m p , math , the quantity more often used in astrophysical theory of galaxy cluster s. This is what astrophysicists refer to as entropy and has units of keV cm sup 2 sup . This quantity relates to the thermodynamic entropy as math S k B ... of K as defined above. Category Astrophysics Category Entropy ... more details
Thermodynamics cTopic Thermodynamic potential Potentials A thermodynamic free entropy is an entropic thermodynamic potential analogous to the thermodynamic free energy free energy . Also known as a Massieu, Planck, or Massieu Planck potentials or functions , or rarely free information. In statistical mechanics, free entropies frequently appear as the logarithm of a Partition function statistical mechanics partition function . In mathematics , free entropy means something quite different it is a generalization of entropy defined in the subject of free probability . A free entropy is generated by a Legendre transform of the entropy. The different potentials correspond to different constraints to which the system may be subjected. Examples see also List of thermodynamic properties The most common examples are class wikitable Name Function Alt. function Natural variables Entropy math S frac 1 T U frac P T V sum i 1 s frac mu i T N i , math align center math U,V, N i , math Massieu potential Helmholtz free entropy math Phi S frac 1 T U math math frac A T math align center math frac 1 T ,V, N i , math Planck potential Gibbs free entropy math Xi Phi frac P T V math math frac G T math align center math frac 1 T , frac P T , N i , math where Col begin Col break math S math is entropy math Phi math is the Massieu potential ref name Planes2000 cite web author Antoni Planes coauthors Eduard Vives date 2000 10 24 publisher Universitat de Barcelona url http www.ecm.ub.es condensed eduard papers massieu node2.html title Entropic variables and Massieu Planck functions accessdate 2007 09 18 ... of the potentials on the natural variables Entropy math S S U,V, N i math By the definition of a total ... Helmholtz free entropy math Phi S frac U T math math Phi frac U T frac P V T sum i 1 s frac mu ... potential Gibbs free entropy math Xi Phi frac P V T math math Xi frac P V T sum i 1 s frac mu i N T frac ... New York isbn 0 471 86256 8 Category Thermodynamic entropy pl Entropia swobodna ... more details
reason, the increase of entropy has begun to accelerate. This effect would cause precarious ecosystems ... managed to regain his sanity, that he realised the entropy effect himself, and began working to undo ... and the acceleration of entropy increase . The strain of so many travels is too much for his .... External links memoryalpha article The Entropy Effect Star Trek publications Star Trek DEFAULTSORT Entropy Effect, The Category Star Trek novels Category Novels by Vonda McIntyre Category ... more details
In statistics , an approximate entropy ApEn is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time series data. ref name Pincus1991 cite journal last1 Pinus first1 S. M. last2 Gladstone first2 I. M. last3 Ehrenkranz first3 R. A. title A REGULARITY STATISTIC FOR MEDICAL DATA ANALYSIS journal Journal of Clinical Monitoring and Computing year 1991 volume 7 issue 4 pages 335 345 DOI 10.1007 BF01619355 ref For example, there are two series of data series 1 10,20,10,20,10,20,10,20,10,20,10,20... , which alternates 10 and 20. series 2 10,10,20,10,20,20,20,10,10,20,10,20,20... , which has either a value of 10 or 20, randomly chose, each with probability 1 2. Moment statistics , such as mean and variance , will not distinguish between these two series. Nor will rank order statistics distinguish between these series. Yet series 1 is perfectly regular knowing one term has the value of 20 enables one to predict with certainty that the next term will have the value of 10. Series 2 is randomly valued knowing one term has the value of 20 gives no insight into what value the next term will have. Regularity was originally measured by exact regularity statistics, which has mainly centered around various entropy measures. ref name Pincus1991 ref However, accurate entropy calculation requires vast amounts of data, and the results will be greatly influenced by system noise ref name Pincus21991 cite journal last1 Pinus first1 S. M. title Approximate entropy as a measure of system complexity journal Proceedings of the National Academy of Sciences ... by modifying an exact regularity statistic, K S entropy . ApEn was initially developed to analyze ... Step 6 math Define approximate entropy math mathrm ApEn math as math mathrm ApEn Phi m r Phi m 1 r ... journal last1 Sabeti first1 Malihe title Entropy and complexity measures for EEG signal classification ... using approximate entropy and sample entropy journal American journal of physiology. Heart and circulatory ... more details
The conditional quantum entropy is an entropy measure used in quantum information theory . It is a generalization of the conditional entropy of classical information theory . The conditional entropy is written math S rho sigma math , or math H rho sigma math , depending on the notation being used for the von Neumann entropy . For the remainder of the article, we use the notation math S rho math for the von Neumann entropy. Definition Given two quantum states math rho math and math sigma math , the von Neumann entropies are math S rho math and math S sigma math . The von Neumann entropy measures how uncertain we are about the value of the state how much the state is a mixed state . The joint quantum entropy math S rho, sigma math measures our uncertainty about the joint system which contains both states. By analogy with the classical conditional entropy, one defines the conditional quantum entropy as math S rho sigma stackrel mathrm def S rho, sigma S sigma math . An equivalent and more intuitive operational definition of the quantum conditional entropy as a measure of the quantum communication cost or surplus when performing quantum state merging was given by Micha Horodecki , Jonathan Oppenheim , and Andreas Winter in their paper Quantum Information can be negative http arxiv.org abs quant ph 0505062 . Properties Unlike the classical conditional entropy , the conditional quantum entropy can be negative. This is true even though the quantum von Neumann entropy of single variable is never negative. The negative conditional entropy is also known as the coherent information, and gives the additional number of bits above the classical limit that can be transmitted in a quantum dense coding protocol. Positive conditional entropy of a state thus means the state cannot reach even the classical limit, while the negative conditional entropy provides for additional information ... Classical to Quantum Shannon Theory , arXiv 1106.1445 . Category Quantum mechanical entropy ... more details
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