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distillation, reflux, and rotary evaporators, several types of condensers are commonly used. The Liebig condenser is simply a straight tube within a cooling water jacket and is the simplest (and relatively least expensive) form of condenser. The Graham condenser is a spiral tube within a water jacket, and the Allihn co...	{ "page_id": 13903462, "title": "Condenser (heat transfer)" }
This also increases the surface area. There is a motorized fan inside the condenser unit near the top, which is covered by some grating to keep any objects from accidentally falling inside on the fan. The fan is used to pull outside cooling air in through the heat exchanger section at the sides and blow it out the top ...	{ "page_id": 13903462, "title": "Condenser (heat transfer)" }
− G x m ˙ c L {\displaystyle \Theta (x)={\frac {T_{H}-T(x)}{T_{H}-T(0)}}=e^{-NTU}=e^{-{\frac {hPx}{{\dot {m}}c}}}=e^{-{\frac {Gx}{{\dot {m}}cL}}}} where: x {\displaystyle x} is the distance from the coolant inlet T ( x ) {\displaystyle T(x)} is the coolant temperature, and T(0) the coolant temperature at its inlet T H ...	{ "page_id": 13903462, "title": "Condenser (heat transfer)" }
The molecular formula C3H6S3 (molar mass: 138.26 g/mol) may refer to: Dimethyl trithiocarbonate 1,3,5-Trithiane	{ "page_id": 24520295, "title": "C3H6S3" }
The molecular formula C5H10O2 (molar mass: 102.13 g/mol) may refer to: tert-Butyl formate Ethyl propionate Hydroxypivaldehyde Isobutyl formate Isopropyl acetate Methylbutanoic acids 2-Methylbutanoic acid (2R)-2-Methylbutanoic acid (2S)-2-Methylbutanoic acid 3-Methylbutanoic acid (isovaleric acid) Methyl butyrate Methyl...	{ "page_id": 12265064, "title": "C5H10O2" }
The International Generic Sample Number or IGSN is a persistent identifier for sample. As an active persistent identifier it can be resolved through the Handle System. The system is used in production by the System for Earth Sample Registration (SESAR), Geoscience Australia, Commonwealth Scientific and Industrial Resea...	{ "page_id": 14231149, "title": "International Generic Sample Number" }
to enter a partnership. Under the partnership, DataCite will provide the IGSN ID registration services and supporting technology to enable the ongoing sustainability of the IGSN PID infrastructure. The IGSN e.V. will facilitate a Community of Communities to promote and support new research and innovation for standard m...	{ "page_id": 14231149, "title": "International Generic Sample Number" }
members. In 2018, the Alfred P. Sloan Foundation awarded Columbia University's Lamont–Doherty Earth Observatory a grant for a project to modernise the IGSN business model and system architecture. The funding from the Sloan Foundation will support a series of workshops, at which international experts will come together ...	{ "page_id": 14231149, "title": "International Generic Sample Number" }
a latitudinal gradient, Geochimica et Cosmochimica Acta, 122, 101–126, https://dx.doi.org/10.1016/j.gca.2013.08.001. This paper contains several samples identified by IGSN. One of them is IGSN: 10.58052/SSH000SUA. Information about this sample can be obtained by resolving the IGSN by adding the URL of the resolver befo...	{ "page_id": 14231149, "title": "International Generic Sample Number" }
the IGSN Global Sample Number. Data Science Journal, 20(33), 1–16. https://doi.org/10.5334/dsj-2021-033	{ "page_id": 14231149, "title": "International Generic Sample Number" }
The molecular formula C5H10O4 (molar mass: 134.13 g/mol, exact mass: 134.0579 u) may refer to: Deoxyribose, or 2-deoxyribose (R)-2,3-Dihydroxyisovalerate Monoacetylglycerol 1,4-Anhydroxylitol, or xylitan	{ "page_id": 12265070, "title": "C5H10O4" }
The molecular formula C5H11N (molar mass: 85.15 g/mol, exact mass: 85.0891 u) may refer to: Piperidine (hexahydropyridine) Cyclopentylamine (cyclopentanamine) 1-Methylpyrrolidine 2-Methylpyrrolidine	{ "page_id": 12265071, "title": "C5H11N" }
In chemistry, homolysis (from Greek ὅμοιος (homoios) 'equal' and λύσις (lusis) 'loosening') or homolytic fission is the dissociation of a molecular bond by a process where each of the fragments (an atom or molecule) retains one of the originally bonded electrons. During homolytic fission of a neutral molecule with an e...	{ "page_id": 1648241, "title": "Homolysis (chemistry)" }
multiple factors: Electronegativity Less electronegative atoms are better stabilizers of radicals, meaning that a bond between two electronegative atoms will have a higher BDE than a similar molecule with two less electronegative atoms. Polarizability The larger the electron cloud, the better an atom can stabilize the ...	{ "page_id": 1648241, "title": "Homolysis (chemistry)" }
== References ==	{ "page_id": 1648241, "title": "Homolysis (chemistry)" }
The molecular formula C5H11NO2 may refer to: β-Alanine ethyl ester Amyl nitrite Isovaline 3-Methyl-GABA N-Methylmorpholine N-oxide Norvaline Pentyl nitrite Trimethylglycine Valine	{ "page_id": 12265073, "title": "C5H11NO2" }
This is a list of substances or materials generally considered discredited. A substance can be discredited in one of three ways: It was widely believed to exist at one time but no longer is. Such substances are often part of an obsolete scientific theory. It was once believed to have drastically different properties fr...	{ "page_id": 927350, "title": "List of discredited substances" }
Food fortification is the addition of micronutrients (essential trace elements and vitamins) to food products. Food enrichment specifically means adding back nutrients lost during food processing, while fortification includes adding nutrients not naturally present. Food manufacturers and governments have used these pra...	{ "page_id": 4597367, "title": "Food fortification" }
micronutrients may cause improper development or even disease. The WHO and FAO, among many other nationally recognized organizations, have recognized that there are over 2 billion people worldwide who have a variety of micronutrient deficiencies. In 1992, 159 countries pledged at the FAO/WHO International Conference on...	{ "page_id": 4597367, "title": "Food fortification" }
in some jurisdictions around the world. A more comprehensive view is given by the online Global Fortification Data Exchange. It indicates which of 197 countries worldwide have mandatory and voluntary food fortification in their datasets and country profiles. The website is maintained by the Food Fortification Initiativ...	{ "page_id": 4597367, "title": "Food fortification" }
into action its Food Fortification Policy which included six fundamental rules. In addition to establishing safety guidelines of food fortification, this policy aimed to ensure that food fortification was solely for when the supplemental micronutrient had a national deficiency and that the food chosen to provide that n...	{ "page_id": 4597367, "title": "Food fortification" }
absorb as much of these vitamins as one would be able to absorb from drinking whole milk. On the other hand, the nutrient added as a fortificant may have a higher bioavailability than from foods, which is the case with folic acid used to increase folate intakes. Phytochemicals such as phytic acid in cereal grains can a...	{ "page_id": 4597367, "title": "Food fortification" }
as strategic marketing schemes to sell their product, there is a lot of work that must go into a product before simply fortifying it. To fortify a product, it must first be proven that the addition of this vitamin or mineral is beneficial to health, safe, and an effective method of delivery. The addition must also abid...	{ "page_id": 4597367, "title": "Food fortification" }
It was discovered in 1821 that goiters could be treated by the use of iodized salts. However, it was not until 1916 that the use of iodized salts could be tested in a research trial as a preventative measure against goiters. By 1924, it became readily available in the US. Currently in Canada and the US, the RDA for iod...	{ "page_id": 4597367, "title": "Food fortification" }
vascular or gastrointestinal diseases. Common diseases which present a high frequency of niacin deficiency include alcoholism, anorexia nervosa, HIV infection, gastrectomy, malabsorptive disorders, certain cancers and their associated treatments. === Vitamin D === Since Vitamin D is a fat-soluble vitamin, it cannot be ...	{ "page_id": 4597367, "title": "Food fortification" }
the properties of resistance to dental caries but avoid the staining caused by fluorosis (a condition caused by excessive fluoride intake). The tolerable upper intake level (UL) set for fluoride ranges from 0.7 mg/day for infants aged 0–6 months and 10 mg/day for adults over the age of 19. == See also == Food additive ...	{ "page_id": 4597367, "title": "Food fortification" }
The molecular formula C5H11NO2S (molar mass: 149.21 g/mol, exact mass: 149.0510 u) may refer to: Methionine, an essential amino acid in humans Penicillamine, a medication	{ "page_id": 12265080, "title": "C5H11NO2S" }
The multiplicative weights update method is an algorithmic technique most commonly used for decision making and prediction, and also widely deployed in game theory and algorithm design. The simplest use case is the problem of prediction from expert advice, in which a decision maker needs to iteratively decide on an exp...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
in computational geometry such as Kenneth Clarkson's algorithm for linear programming (LP) with a bounded number of variables in linear time. Later, Bronnimann and Goodrich employed analogous methods to find set covers for hypergraphs with small VC dimension. In operations research and on-line statistical decision maki...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
retained. Experts who make mistakes will be dismissed. For every decision, the aggregator decides by taking a majority vote among the remaining experts. Therefore, every time the aggregator makes a mistake, at least half of the remaining experts are dismissed. The aggregator makes at most log2(N) mistakes. === Weighted...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
every expert i that predicted wrongly, decrease his weight for the next round by multiplying it by a factor of (1-η): w i t + 1 {\displaystyle w_{i}^{t+1}} = ( 1 − η ) w i t {\displaystyle (1-\eta )w_{i}^{t}} (update rule) If η = 0 {\displaystyle \eta =0} , the weight of the expert's advice will remain the same. When η...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
1 with probability q 1 W 0 otherwise {\displaystyle f(x)={\begin{cases}1&{\text{with probability}}{\frac {q_{1}}{W}}\\0&{\text{otherwise}}\end{cases}}} where W = ∑ i w i = q 0 + q 1 {\displaystyle W=\sum _{i}{w_{i}}=q_{0}+q_{1}} . The number of mistakes made by the randomized weighted majority algorithm is bounded as: ...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
we were given the distribution P {\displaystyle P} on experts. Let A {\displaystyle A} = payoff matrix of a finite two-player zero-sum game, with n {\displaystyle n} rows. When the row player p r {\displaystyle p_{r}} uses plan i {\displaystyle i} and the column player p c {\displaystyle p_{c}} uses plan j {\displaysty...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
\delta >0} be an error parameter. To solve the zero-sum game bounded by additive error of δ {\displaystyle \delta } , λ ∗ − δ ≤ min i A ( i , q ) {\displaystyle \lambda ^{}-\delta \leq \min _{i}A\left(i,q\right)} max j A ( p , j ) ≤ λ ∗ + δ {\displaystyle \max _{j}A\left(p,j\right)\leq \lambda ^{}+\delta } So there i...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
j {\displaystyle j} . Without loss of generality, assume the total weight is 1 so that they form a distribution. Thus, for notational convenience, redefine a j {\displaystyle a_{j}} to be l j a j {\displaystyle l_{j}a_{j}} , the problem reduces to finding a solution to the following LP: ∀ j = 1 , 2 , … , m : a j x ≥ 0 ...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
i t Φ t {\displaystyle p_{i}^{t}={\frac {w_{i}^{t}}{\Phi t}}} where Φ t = ∑ i w i t {\displaystyle \Phi t=\sum _{i}w_{i}^{t}} . 2. Observe the cost of the decision m t {\displaystyle m^{t}} . 3. Set w i t + 1 = w i t exp ⁡ ( − η m i t {\displaystyle w_{i}^{t+1}=w_{i}^{t}\exp(-\eta m_{i}^{t}} ). ==== AdaBoost algorithm ...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
with the distribution p t {\displaystyle p^{t}} ; get back a hypothesis h t : X → {\displaystyle h_{t}:X\rightarrow } [0,1]. 3. Calculate the error of h t : ϵ t = ∑ i = 1 N p i t \| h t ( x i ) − y i \| {\displaystyle h_{t}:\epsilon _{t}=\sum _{i=1}^{N}p_{i}^{t}\|h_{t}(x_{i})-y_{i}\|} . 4. Set β t = ϵ t 1 − ϵ t {\displayst...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
==== Solution ==== Given vector p ∈ Δ n {\displaystyle p\in \Delta _{n}} , solves the following relaxed problem ∃ ? x : p T A x ≥ p T b {\displaystyle \exists ?x:p^{\textsf {T}}\!\!Ax\geq p^{\textsf {T}}\!b} (2) If there exists a x satisfying (1), then x satisfies (2) for all p ∈ Δ n {\displaystyle p\in \Delta _{n}} . ...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
VC dimension. Gradient descent method Matrix multiplicative weights update Plotkin, Shmoys, Tardos framework for packing/covering LPs Approximating multi-commodity flow problems O (logn)- approximation for many NP-hard problems Learning theory and boosting Hard-core sets and the XOR lemma Hannan's algorithm and multipl...	{ "page_id": 52242050, "title": "Multiplicative weight update method" }
The grain per gallon (gpg) is a unit of water hardness defined as 1 grain (64.8 milligrams) of calcium carbonate dissolved in 1 US gallon of water (3.785412 L). It translates into 1 part in about 58,000 parts of water or 17.1 parts per million (ppm). Also called Clark degree (in terms of an imperial gallon). == Usage =...	{ "page_id": 27797122, "title": "Grain per gallon" }
The Oskar Klein Memorial Lecture at Stockholm University, dedicated to the memory of the Swedish physicist Oskar Klein (1894-1977), is held annually since 1988 by a prominent physicist, who also receives the Oskar Klein Medal. The lecture is sponsored by the university and the Nobel Committee of the Royal Swedish Acade...	{ "page_id": 3417735, "title": "Oskar Klein Memorial Lecture" }
Barnaviridae is a family of non-enveloped, positive-strand RNA viruses. Cultivated mushrooms serve as natural hosts. The family has one genus, Barnavirus, which contains one species: Mushroom bacilliform virus. Diseases associated with this family includes La France disease. == Structure == Viruses in Barnaviridae are ...	{ "page_id": 1582728, "title": "Barnaviridae" }
The International Society for Phylogenetic Nomenclature was established to encourage and facilitate the development and use of, and communication about, phylogenetic nomenclature. It organizes periodic scientific meetings and is overseeing the completion and implementation of the PhyloCode. == History and meetings == T...	{ "page_id": 10954379, "title": "International Society for Phylogenetic Nomenclature" }
This is a list of common physical constants and variables, and their notations. Note that bold text indicates that the quantity is a vector. == Latin characters == == Greek characters == == Other characters == == See also == List of letters used in mathematics and science Glossary of mathematical symbols List of mathem...	{ "page_id": 7153296, "title": "List of common physics notations" }
Radford M. Neal (born September 12, 1956) is a professor emeritus at the Department of Statistics and Department of Computer Science at the University of Toronto, where he held a Canada research chair in statistics and machine learning. == Education and career == Neal studied computer science at the University of Calga...	{ "page_id": 46605971, "title": "Radford M. Neal" }
Dayan, Peter; Frey, Brendan J.; Neal, Radford M. (1995-05-26). "The "Wake-Sleep" Algorithm for Unsupervised Neural Networks". Science. 268 (5214): 1158–1161. Bibcode:1995Sci...268.1158H. doi:10.1126/science.7761831. ISSN 0036-8075. PMID 7761831. S2CID 871473. Dayan, Peter; Hinton, Geoffrey E.; Neal, Radford M.; Zemel, ...	{ "page_id": 46605971, "title": "Radford M. Neal" }
The molecular formula C2532H3854N672O711S16 (molar mass: 55597.4 g/mol) may refer to: Alglucerase Imiglucerase	{ "page_id": 61154967, "title": "C2532H3854N672O711S16" }
Amorphous carbonia, also called a-carbonia or a-CO2, is an exotic amorphous solid form of carbon dioxide that is analogous to amorphous silica glass. It was first made in the laboratory in 2006 by subjecting dry ice to high pressures (40-48 gigapascal, or 400,000 to 480,000 atmospheres), in a diamond anvil cell. Amorph...	{ "page_id": 5580444, "title": "Amorphous carbonia" }
Karyogamy is the final step in the process of fusing together two haploid eukaryotic cells, and refers specifically to the fusion of the two nuclei. Before karyogamy, each haploid cell has one complete copy of the organism's genome. In order for karyogamy to occur, the cell membrane and cytoplasm of each cell must fuse...	{ "page_id": 599709, "title": "Karyogamy" }
and instead creates variation within the somatic cells of an already developed organism, such as a fungus. == Role in sexual reproduction == The role of karyogamy in sexual reproduction can be demonstrated most simply by single-celled haploid organisms such as the algae of genus Chlamydomonas or the yeast Saccharomyces...	{ "page_id": 599709, "title": "Karyogamy" }
zygote, or a zygospore, which can then enter meiosis, a process of chromosome duplication, recombination, and cell division, to create four new haploid gamete cells. One possible advantage of sexual reproduction is that it results in more genetic variability, providing the opportunity for adaptation through natural sel...	{ "page_id": 599709, "title": "Karyogamy" }
a structure known as the half-bridge. Other proteins, such as Kar9 and Bim1 in yeast, attach to the plus end of the microtubules. They are activated by pheromone signals to attach to the shmoo tip. A shmoo is a projection of the cellular membrane which is the site of initial cell fusion in plasmogamy. After plasmogamy,...	{ "page_id": 599709, "title": "Karyogamy" }
fusion of the outer membrane, fusion of the inner membrane, and fusion of the spindle pole bodies. In yeast, several members of the Kar family of proteins, as well as a protamine, are required for the fusion of nuclear membranes. The protamine Prm3 is located on the outer surface of each nuclear membrane, and is requir...	{ "page_id": 599709, "title": "Karyogamy" }
usually innocuous, C. albicans can turn pathogenic and is a particular problem in immunosuppressed patients. Unlike with most other fungi, diploid cells of different mating types fuse to create tetraploid cells which subsequently return to the diploid state by losing chromosomes. == Similarities to and differences from...	{ "page_id": 599709, "title": "Karyogamy" }
In chemistry, electron counting is a formalism for assigning a number of valence electrons to individual atoms in a molecule. It is used for classifying compounds and for explaining or predicting their electronic structure and bonding. Many rules in chemistry rely on electron-counting: Octet rule is used with Lewis str...	{ "page_id": 9890, "title": "Electron counting" }
on the periodic table and determining the number of its valence electrons. One counts valence electrons for main group elements differently from transition metals, which use d electron count. E.g. in period 2: B, C, N, O, and F have 3, 4, 5, 6, and 7 valence electrons, respectively. E.g. in period 4: K, Ca, Sc, Ti, V, ...	{ "page_id": 9890, "title": "Electron counting" }
the metal-ligand ensemble. An example of this complication is the M–NO entity. When this grouping is linear, the NO ligand is considered to be a three-electron ligand. When the M–NO subunit is strongly bent at N, the NO is treated as a pseudohalide and is thus a one electron (in the neutral counting approach). The situ...	{ "page_id": 9890, "title": "Electron counting" }
the duet rule for hydrogen, and hence is expected to be a stable molecule (as we see from daily life) H2S, for the central S neutral counting: S contributes 6 electrons, each hydrogen radical contributes one each: 6 + 2 × 1 = 8 valence electrons ionic counting: S2− contributes 8 electrons, each proton contributes 0: 8 ...	{ "page_id": 9890, "title": "Electron counting" }
ligands are L-type ligand neutral ligands, thus contributing two electrons each. The two chloride ligands hallides and thus 1 electron donors, donating 1 electron each to the electron count. The total electron count of RuCl2(bpy)2 is 18. In the ionic counting method, the Ruthenium of the complex is treated as Ru(II). I...	{ "page_id": 9890, "title": "Electron counting" }
× 6 = 18 valence electrons on iron. conclusion: Ferrocene is expected to be an isolable compound. == See also == d electron count Tolman's rule == References ==	{ "page_id": 9890, "title": "Electron counting" }
In chemistry, heterolysis or heterolytic fission (from Greek ἕτερος (heteros) 'different' and λύσις (lusis) 'loosening') is the process of cleaving/breaking a covalent bond where one previously bonded species takes both original bonding electrons from the other species. During heterolytic bond cleavage of a neutral mol...	{ "page_id": 1648291, "title": "Heterolysis (chemistry)" }
of the covalent bond. The limiting reaction step is generally the formation of ion pairs. One group in Ukraine did an in-depth study on the role of nucleophilic solvation and its effect on the mechanism of bond heterolysis. They found that the rate of heterolysis depends strongly on the nature of the solvent. For examp...	{ "page_id": 1648291, "title": "Heterolysis (chemistry)" }
Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of info...	{ "page_id": 9891, "title": "Entropy" }
which has become one of the defining universal constants for the modern International System of Units. == History == In his 1803 paper Fundamental Principles of Equilibrium and Movement, the French mathematician Lazare Carnot proposed that in any machine, the accelerations and shocks of the moving parts represent losse...	{ "page_id": 9891, "title": "Entropy" }
that no change occurs in the working body, and gave that change a mathematical interpretation, by questioning the nature of the inherent loss of usable heat when work is done, e.g., heat produced by friction. He described his observations as a dissipative use of energy, resulting in a transformation-content (Verwandlun...	{ "page_id": 9891, "title": "Entropy" }
1865, Clausius named the concept of "the differential of a quantity which depends on the configuration of the system", entropy (Entropie) after the Greek word for 'transformation'. He gave "transformational content" (Verwandlungsinhalt) as a synonym, paralleling his "thermal and ergonal content" (Wärme- und Werkinhalt)...	{ "page_id": 9891, "title": "Entropy" }
phenomenon as expressed in the second law of thermodynamics, which has found universal applicability to physical processes. === State variables and functions of state === Many thermodynamic properties are defined by physical variables that define a state of thermodynamic equilibrium, which essentially are state variabl...	{ "page_id": 9891, "title": "Entropy" }
occurs without any dissipation, deviating only infinitesimally from the thermodynamic equilibrium), and it may conserve total entropy. For example, in the Carnot cycle, while the heat flow from a hot reservoir to a cold reservoir represents the increase in the entropy in a cold reservoir, the work output, if reversibly...	{ "page_id": 9891, "title": "Entropy" }
in the system was conserved. But in fact, the magnitude of heat Q H {\textstyle Q_{\mathsf {H}}} is greater than the magnitude of heat Q C {\textstyle Q_{\mathsf {C}}} . Through the efforts of Clausius and Kelvin, the work W {\textstyle W} done by a reversible heat engine was found to be the product of the Carnot effic...	{ "page_id": 9891, "title": "Entropy" }
C \| = W − Q H − Q C = 0 {\displaystyle W-Q_{\Sigma }=W-\left\vert Q_{\mathsf {H}}\right\vert +\left\vert Q_{\mathsf {C}}\right\vert =W-Q_{\mathsf {H}}-Q_{\mathsf {C}}=0} Since this equality holds over an entire Carnot cycle, it gave Clausius the hint that at each stage of the cycle the difference between a work and a n...	{ "page_id": 9891, "title": "Entropy" }
S r , i = − Q i / T i {\textstyle \Delta S_{{\mathsf {r}},i}=-Q_{i}/T_{i}} , where i {\textstyle i} is either H {\textstyle {\mathsf {H}}} for a hot reservoir or C {\textstyle {\mathsf {C}}} for a cold one. If we consider a heat engine which is less effective than Carnot cycle (i.e., the work W {\textstyle W} produced ...	{ "page_id": 9891, "title": "Entropy" }
the early 1850s by Rudolf Clausius and essentially describes how to measure the entropy of an isolated system in thermodynamic equilibrium with its parts. Clausius created the term entropy as an extensive thermodynamic variable that was shown to be useful in characterizing the Carnot cycle. Heat transfer in the isother...	{ "page_id": 9891, "title": "Entropy" }
energy divided by temperature, and the unit joule per kelvin (J/K) in the International System of Units (SI). To find the entropy difference between any two states of the system, the integral must be evaluated for some reversible path between the initial and final states. Since an entropy is a state function, the entro...	{ "page_id": 9891, "title": "Entropy" }
Ludwig Boltzmann in the 1870s by analysing the statistical behaviour of the microscopic components of the system. Boltzmann showed that this definition of entropy was equivalent to the thermodynamic entropy to within a constant factor—known as the Boltzmann constant. In short, the thermodynamic definition of entropy pr...	{ "page_id": 9891, "title": "Entropy" }
of a substance is usually given as an intensive property — either entropy per unit mass (SI unit: J⋅K−1⋅kg−1) or entropy per unit amount of substance (SI unit: J⋅K−1⋅mol−1). Specifically, entropy is a logarithmic measure for the system with a number of states, each with a probability p i {\textstyle p_{i}} of being occ...	{ "page_id": 9891, "title": "Entropy" }
In what has been called the fundamental postulate in statistical mechanics, among system microstates of the same energy (i.e., degenerate microstates) each microstate is assumed to be populated with equal probability p i = 1 / Ω {\textstyle p_{i}=1/\Omega } , where Ω {\textstyle \Omega } is the number of microstates wh...	{ "page_id": 9891, "title": "Entropy" }
set of macroscopic variables to describe the system, i.e. every independent parameter that may change during experiment. Entropy can also be defined for any Markov processes with reversible dynamics and the detailed balance property. In Boltzmann's 1896 Lectures on Gas Theory, he showed that this expression gives a mea...	{ "page_id": 9891, "title": "Entropy" }
thermodynamic system is a measure of how far the equalisation has progressed. Thermodynamic entropy is a non-conserved state function that is of great importance in the sciences of physics and chemistry. Historically, the concept of entropy evolved to explain why some processes (permitted by conservation laws) occur sp...	{ "page_id": 9891, "title": "Entropy" }
is at maximum entropy and cannot drive a heat engine. A substance at non-uniform temperature is at a lower entropy (than if the heat distribution is allowed to even out) and some of the thermal energy can drive a heat engine. A special case of entropy increase, the entropy of mixing, occurs when two or more different s...	{ "page_id": 9891, "title": "Entropy" }
under the following postulates: == Second law of thermodynamics == The second law of thermodynamics requires that, in general, the total entropy of any system does not decrease other than by increasing the entropy of some other system. Hence, in a system isolated from its environment, the entropy of that system tends n...	{ "page_id": 9891, "title": "Entropy" }
at temperature T {\textstyle T} absorbing an infinitesimal amount of heat δ q {\textstyle \delta q} in a reversible way, is given by δ q / T {\textstyle \delta q/T} . More explicitly, an energy T R S {\textstyle T_{R}S} is not available to do useful work, where T R {\textstyle T_{R}} is the temperature of the coldest a...	{ "page_id": 9891, "title": "Entropy" }
volume V {\textstyle V} as the only external parameter, this relation is: d U = T d S − p d V {\displaystyle \mathrm {d} U=T\ \mathrm {d} S-p\ \mathrm {d} V} Since both internal energy and entropy are monotonic functions of temperature T {\textstyle T} , implying that the internal energy is fixed when one specifies the...	{ "page_id": 9891, "title": "Entropy" }
J⋅kg−1⋅K−1). Alternatively, in chemistry, it is also referred to one mole of substance, in which case it is called the molar entropy with a unit of J⋅mol−1⋅K−1. Thus, when one mole of substance at about 0 K is warmed by its surroundings to 298 K, the sum of the incremental values of q r e v / T {\textstyle q_{\mathsf {...	{ "page_id": 9891, "title": "Entropy" }
(spontaneous) process, while a positive ΔG denotes a non-spontaneous one. When both ΔH and ΔS are positive (endothermic, entropy-increasing), the reaction becomes spontaneous at sufficiently high temperatures, as the TΔS term dominates. Conversely, if both ΔH and ΔS are negative (exothermic, entropy-decreasing), sponta...	{ "page_id": 9891, "title": "Entropy" }
{\textstyle P{\dot {V}}} across the system boundaries cause changes in the entropy of the system. Heat transfer entails entropy transfer Q ˙ / T {\textstyle {\dot {Q}}/T} , where T {\textstyle T} is the absolute thermodynamic temperature of the system at the point of the heat flow. If there are mass flows across the sy...	{ "page_id": 9891, "title": "Entropy" }
g e n {\displaystyle {\frac {\mathrm {d} S}{\mathrm {d} t}}=\sum _{k=1}^{K}{{\dot {M}}_{k}{\hat {S}}_{k}+{\frac {\dot {Q}}{T}}+{\dot {S}}_{\mathsf {gen}}}} where ∑ k = 1 K M ˙ k S ^ k {\textstyle \sum _{k=1}^{K}{{\dot {M}}_{k}{\hat {S}}_{k}}} is the net rate of entropy flow due to the flows of mass M ˙ k {\textstyle {\...	{ "page_id": 9891, "title": "Entropy" }
constant composition, the entropy changes are given by simple formulas. === Isothermal expansion or compression of an ideal gas === For the expansion (or compression) of an ideal gas from an initial volume V 0 {\textstyle V_{0}} and pressure P 0 {\textstyle P_{0}} to a final volume V {\textstyle V} and pressure P {\tex...	{ "page_id": 9891, "title": "Entropy" }
a state function, the entropy change of any process in which temperature and volume both vary is the same as for a path divided into two steps – heating at constant volume and expansion at constant temperature. For an ideal gas, the total entropy change is: Δ S = n C V ln ⁡ T T 0 + n R ln ⁡ V V 0 {\displaystyle \Delta ...	{ "page_id": 9891, "title": "Entropy" }
of disorder in the universe or of the availability of the energy in a system to do work. a measure of a system's thermal energy per unit temperature that is unavailable for doing useful work. In Boltzmann's analysis in terms of constituent particles, entropy is a measure of the number of possible microscopic states (or...	{ "page_id": 9891, "title": "Entropy" }
of the system, an expression similar to Shannon's channel capacity, and C O {\textstyle C_{\mathsf {O}}} is the "order" capacity of the system. === Energy dispersal === The concept of entropy can be described qualitatively as a measure of energy dispersal at a specific temperature. Similar terms have been in use from e...	{ "page_id": 9891, "title": "Entropy" }
parcel of intermediate temperature, in which the overall increase in entropy represents a "loss" that can never be replaced. As the entropy of the universe is steadily increasing, its total energy is becoming less useful. Eventually, this is theorised to lead to the heat death of the universe. === Entropy and adiabatic...	{ "page_id": 9891, "title": "Entropy" }
as "von Neumann entropy": S = − k B t r ( ρ ^ × ln ⁡ ρ ^ ) {\displaystyle S=-k_{\mathsf {B}}\ \mathrm {tr} {\left({\hat {\rho }}\times \ln {\hat {\rho }}\right)}} where ρ ^ {\textstyle {\hat {\rho }}} is the density matrix, t r {\textstyle \mathrm {tr} } is the trace operator and k B {\textstyle k_{\mathsf {B}}} is the...	{ "page_id": 9891, "title": "Entropy" }
p ( x i ) log ⁡ p ( x i ) {\displaystyle H(X)=-\sum _{i=1}^{n}{p(x_{i})\log {p(x_{i})}}} where the base of the logarithm determines the units (for example, the binary logarithm corresponds to bits). In the case of transmitted messages, these probabilities were the probabilities that a particular message was actually tr...	{ "page_id": 9891, "title": "Entropy" }
particles N {\textstyle N} and constant volume V {\textstyle V} , and it uses the definition of temperature in terms of entropy, while limiting energy exchange to heat d U → d Q {\textstyle \mathrm {d} U\rightarrow \mathrm {d} Q} : T := ( ∂ U ∂ S ) V , N ⇒ ⋯ ⇒ d S = d Q T {\displaystyle T:={\left({\frac {\partial U}{\p...	{ "page_id": 9891, "title": "Entropy" }
this perspective, entropy measurement is thought of as a clock in these conditions. Since the 19th century, a number the philosophers have drawn upon the concept of entropy to develop novel metaphysical and ethical systems. Examples of this work can be found in the thought of Friedrich Nietzsche and Philipp Mainländer,...	{ "page_id": 9891, "title": "Entropy" }
are totally effective matter and energy traps. However, the escape of energy from black holes might be possible due to quantum activity (see Hawking radiation). The role of entropy in cosmology remains a controversial subject since the time of Ludwig Boltzmann. Recent work has cast some doubt on the heat death hypothes...	{ "page_id": 9891, "title": "Entropy" }
== Notes == == References == David, Kover (14 August 2018). "Entropia – fyzikálna veličina vesmíru a nášho života". stejfree.sk. Archived from the original on 27 May 2022. Retrieved 13 April 2022. == Further reading == == External links == "Entropy" at Scholarpedia Entropy and the Clausius inequality MIT OCW lecture, p...	{ "page_id": 9891, "title": "Entropy" }
The Institute of Chemistry of Ireland (ICI) is a society representing chemists in Ireland. It is led by Celine Marmion, a Professor of Chemistry at the Royal College of Surgeons in Ireland. == History == The first meeting was held on 15 May 1922. This meeting led to the formation of The Chemical Association of Ireland ...	{ "page_id": 45229736, "title": "Institute of Chemistry of Ireland" }
Anila Paparisto is an entomologist and taxonomist from Albania, who was appointed in 2021 as Vice Rector for Teaching at the University of Tirana. She is also Professor in Invertebrate Zoology and Teaching Didactics there. Her career began at the university in 1994 and in 2011 was promoted to professor. Her research ha...	{ "page_id": 68560555, "title": "Anila Paparisto" }
The Enterosoma genetic code (tentative code number 34) translates AGG to methionine, as determined by the codon assignment software Codetta; it was further shown that this recoding is associated with a special tRNA with the appropriate anticodon and tRNA identity elements. The code is found in a small clade of species ...	{ "page_id": 77670060, "title": "Enterosoma genetic code" }

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