
Review of Short Phrases and Links 
This Review contains major "Entropy" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 Entropy is a concept in thermodynamics (see thermodynamic entropy), statistical mechanics and information theory.
 Entropy is a measure of disorder: cells are NOT disordered and so have low entropy.
 Entropy is a measure of evenness of a distribution of energy between parts of a system.
 ENTROPY is a measure of the unavailability of energy in a substance.
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 Entropy is a measure of the amount of disorder in a system, and an entropic force would tend to move things toward the most disorderly arrangement.
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 Thus, in the Carnot cycle, which is reversible, there is no change in the total entropy.
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 Mixing paradox: On the change of entropy of a system before and after mixing.
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 The average information going across the channel, the entropy, goes down, with no relationship to the amount of energy needed to cut the wire.
 In this experiment, a direct relationship between information and another physical property, entropy, is demonstrated.
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 Thus, we would expect there to be some relationship between temperature and entropy.
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 In this paper a unified formulation of subsethood, entropy, and cardinality for intervalvalued fuzzy sets (IVFSs) is presented.
 As a consequence, lower bounds for the topological entropy of transitive graph maps in terms of the cardinality of their splittings are obtained.
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 It includes a calculation of the entropy of black holes.
 The possibility for application of the proposed approach to the calculation of quantum entropy of a black hole is considered.
 One of the results that is of most interest is his outline of the calculation of black hole entropy by counting states.
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 Duality predicts that the entropy of these black holes is related to the quartic invariant of the E(7,7) group.
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 By the Aether Wave Theory the same duality exist between the energy and entropy, as between potential and kinetic energy.
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 One must take care in trying to apply properties of discrete entropy to differential entropy, since probability density functions can be greater than 1.
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 One measure which does so is the discrete entropy.
 Often, information entropy is measured in shannons, whereas the (discrete) storage space of digital devices is measured in bits.
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 The following is a list of additional definitions of entropy from a collection of textbooks.
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 Entropy has a precise definition within physics: it refers to the concentration or dispersal of energy at a molecular level.
 Since a finite universe is an isolated system then, by the Second Law of Thermodynamics, its total entropy is constantly increasing.
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 But entropy is increasing as the universe evolves, just like the Second Law of Thermodynamics says it should.
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 When heat is added to a system at high temperature, the increase in entropy is small.
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 Calculating the entanglement entropy between spatially separated regions allows us to probe the topological order in Laughlin and MooreRead states.
 Besides this, the law predicts that the entropy of an isolated system always increases with time.
 Having each "causal patch" become a separate universe allows each universe to contract essentially empty of matter and entropy.
 If you took all of the matter in our observable universe and made one big black hole, the entropy would be about 10 120.
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 The entropy is normalized by the variance of the component, so absolute scale doesn't matter.
 Thus, part of the fluid system's mass is transferred without any energy transfer (since the superfluid has zero entropy).
 Using the first law of black hole mechanics, it follows that the entropy of a black hole is one quarter of the area of the horizon.
 However, the entropy from the previous cycle is spread to regions beyond the horizon during the period of dark energy domination.
 The generic patch contains no quark, lepton or force carrier only dark energy and its entropy thereby vanishes.
 The only way to understand the origin of entropy is to understand the origin of the universe  by asking what happened at the Big Bang, and even before.
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 A corollary holds the initial singularity to have minimum entropy which then rapidly increases during the first moments of the Big Bang.
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 Frampton and Baum circumvent the Big Bang by postulating that, at the turnaround, any remaining entropy is in patches too remote for interaction.
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 A key measure of information in the theory is known as entropy, which is usually expressed by the average number of bits needed for storage or communication.
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 The entropy associated with these degrees of freedom matches with the Wald entropy for the theory.
 This results in an "entropy gap" pushing the system further away from equilibrium.
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Related
 The entropy of a system is related to the amount of information it contains.
 For molecular systems, uncertainty is closely related to entropy and hence has clear connections to the Second Law of Thermodynamics.
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 This principle is vitally important to understanding the behavior of a quantity closely related to energy, called entropy.
 Fisher introduced the concept of Fisher information in 1925, many years before Shannon 's notion of entropy.
 Information entropy is available as a measure of statistical dispersion, but no notion of standard deviation or the like exists.
 In his recently developed theory of free probability and free entropy, Voiculescu introduces a notion of free entropy dimension.
 If you own a textbook with data for enthalpy and entropy, you can use this equation to predict whether or not a chemical reaction can proceed spontaneously.
 According to Equation (2) entropy falls as the temperature from the hot combustion source, T H, increases.
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 In addition, the reduction of complexity, Q, reduces the entropy due to the second term in Equation (29).
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 Mathematically, a coin flip is an example of a Bernoulli trial, and its entropy is given by the binary entropy function.
 He knew how the entropy of the radiation had to depend mathematically upon its energy in the highfrequency region if Wien's law held there.
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 For example, a fair coin flip (2 equally likely outcomes) will have less entropy than a roll of a die (6 equally likely outcomes).
 The said quantity is amount of entropy that may be increased without changing an internal energy or increasing its volume.
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 The entropy of a system depends on its internal energy and the external parameters, such as the volume.
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 Here, U is internal energy, T is temperature, S is entropy, p is pressure, and V is volume.
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 Entropy and generators for locally compact subshifts, Ergod.Th.
 It is believed that free entropy dimension of the generators of a factor of type II 1 is closely related to the minimal number of generators of the factor.
 All the bits of the input string are assumed to be equally random, even though the entropy present in the random source may be limited.
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 A known configuration of classical fields has zero entropy: there is nothing random about electric and magnetic fields, or gravitational waves.
 In information theory, the cross entropy between two probability distributions measures the overall difference between the two distributions.
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 Entropy is maximized when the probability distribution is uniform.
 The fluctuation theorem is a statement concerning the probability distribution of the timeaveraged irreversible entropy production [1], denoted.
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 The subkey generation process is designed to preserve the entire entropy of the key and to distribute that entropy uniformly throughout the subkeys.
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 In a cryptosystem, entropy is the amount of disorder or randomness present in a key or in the phrase used to generate a key.
 The strength of the encrypted text is determined by the entropy, or degree of uncertainty, in the key and the algorithm.
 If, in addition, there are mass flows across the system boundaries, the total entropy of the system will also change due to this convected flow.
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 Law #2 (Entropy): All things (mass and energy) tend toward disorder.
 Hence the surface area of a black hole is directly proportional not only to its entropy, but to its time dimension and its mass as well.
 Therefore, Jacob Bekenstein proposed that a black hole should have an entropy and that it should be proportional to its horizon area.
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 A calculation within ChernSimons theory leads to the desired result for the entropy, proportional to the horizon area.
 LQG may or may not be viable as a refinement of either gravity or geometry; entropy is calculated for a kind of hole which may or may not be a black hole.
 This effect of gravity has allowed the entropy of the universe to fall from its initial high value which was due to the unitial temperature uniformity.
 Since Bekenstein and Hawking computed the entropy of a black hole, this computation has become a crucial litmus test for any theory of quantum gravity.
 But the entropy was lower in the past, and to understand that empirical feature of the universe we have to think about cosmology.
 Any questions?" Actually, as Woit states: "I don’t disagree that to understand cosmology you want to explain the low entropy at the Big Bang.
 If you prefer it, I would say that string theory is the only theory of quantum gravity that has a fundmanetal derivation of the entropy of any black hole.
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 The oneloop contribution to the entropy of a black hole from field modes near the horizon is computed in string theory.
 In addition we have calculated correction to the entropy from alpha'^3*R^4 terms coming from string theory.
 The measure should be continuous, so that changing the values of the probabilities by a very small amount should only change the entropy by a small amount.
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 Intuitively, entropy quantifies the uncertainty involved when encountering a random variable.
 Entropy is also the shortest average message length, in bits, that can be sent to communicate the true value of the random variable to a recipient.
 That is, we use the entropy of the random variable S in order to save truly random bits later on.
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 We can use Lagrange multipliers to find the point of maximum entropy (depending on the probabilities).
 For a given mean and variance, the corresponding normal distribution is the continuous distribution with the maximum entropy.
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 Thus, as long suspected, black holes have the maximum entropy for given mass and size which is allowed by quantum theory and general relativity.
 If a system is at equilibrium, by definition no spontaneous processes occur, and therefore the system is at maximum entropy.
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 While the random number generator was used to generate 128bit keys, the maximum entropy was around 20 bits.
 Randomly generated keys aren't necessarily better, because now the random number generator must produce keys with maximum entropy.
 In this case, the entropy increases with the number of outcomes.
 If all the outcomes (letters in the example above) are equally likely then increasing the number of letters should always increase the entropy.
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 Such choices may be considered to add information that reduces the entropy (related to number of internal choices) to produce the same external product line.
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 The independent components are random variables of minimum entropy constructed from linear combinations of the input features.
 Hamming distance Joint entropy – is the measure how much entropy is contained in a joint system of two random variables.
 Entropy change has often been defined as a change to a more disordered state at a molecular level.
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 The fragility of the liquid is, in this case, controlled by the entropy change in the elementary excitation process.
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 We can now deduce an important fact about the entropy change during any thermodynamic transformation, not just a cycle.
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 The thermodynamic concept of entropy can be described qualitatively as a measure of energy dispersal at a specific temperature.
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Categories
 Theoretical Physics > Relativity > General Relativity > Black Holes
 Measure
 Encyclopedia of Finance. > Technology > Energy
 Encyclopedia of Keywords > Nature > Systems > System
 Random Variable
Related Keywords
* Arrow
* Bit
* Bits
* Black Hole
* Black Holes
* Black Hole Entropy
* Boltzmann
* Change
* Character
* Classical Thermodynamics
* Clausius
* Closed System
* Concept
* Conserved
* Decrease
* Definition
* Density Matrix
* Disorder
* Disordered
* Energy
* Enthalpy
* Equilibrium State
* Estimate
* Fair Coin
* Free Energy
* Function
* Hawking Radiation
* Information
* Information Content
* Information Entropy
* Information Theory
* Internal Energy
* Logarithm
* Long String
* Loop Quantum Gravity
* Measure
* Net Change
* Probability
* Pure State
* Quantity
* Radiant Energy
* Randomness
* Second Law
* Shannon
* Source
* State
* Statistical Mechanics
* System
* Systems
* Temperature
* Terms
* Thermal Energy
* Thermodynamic
* Thermodynamics
* Thermodynamic Entropy
* Thermodynamic Equilibrium
* Uncertainty
* Universe
* Wip
* Work
* Zero
* Zero Entropy

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