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17,300 | Since the latter is valid over the entire cycle, this gave Clausius the hint that at each stage of the cycle, work and heat would not be equal, but rather their difference would be the change of a state function that would vanish upon completion of the cycle. The state function was called the internal energy, that is c... | https://en.wikipedia.org/wiki?curid=9891 |
17,301 | This implies that there is a function of state whose change is and this state function is conserved over a complete Carnot cycle, like other state function such as the internal energy. Clausius called this state function "entropy". One can see that entropy was discovered through mathematics rather than through laborato... | https://en.wikipedia.org/wiki?curid=9891 |
17,302 | where we denote an entropy change for a thermal reservoir by , for "i" as either H (Hot reservoir) or C (Cold reservoir), by considering the abovementioned signal convention of heat for the engine. | https://en.wikipedia.org/wiki?curid=9891 |
17,303 | Clausius then asked what would happen if less work is produced by the system than that predicted by Carnot's principle for the same thermal reservoir pair and the same heat transfer from the hot reservoir to the engine . In this case, the right-hand side of the equation () would be the upper bound of the work output by... | https://en.wikipedia.org/wiki?curid=9891 |
17,304 | telling that the magnitude of the entropy earned by the cold reservoir is greater than the entropy lost by the hot reservoir. The net entropy change in the engine per its thermodynamic cycle is zero, so the net entropy change in the engine and both the thermal reservoirs per cycle increases if work produced by the engi... | https://en.wikipedia.org/wiki?curid=9891 |
17,305 | The Carnot cycle and Carnot efficiency as shown in the equation () are useful because they define the upper bound of the possible work output and the efficiency of any classical thermodynamic heat engine. Other cycles, such as the Otto cycle, Diesel cycle and Brayton cycle, can be analyzed from the standpoint of the Ca... | https://en.wikipedia.org/wiki?curid=9891 |
17,306 | For very small numbers of particles in the system, statistical thermodynamics must be used. The efficiency of devices such as photovoltaic cells requires an analysis from the standpoint of quantum mechanics. | https://en.wikipedia.org/wiki?curid=9891 |
17,307 | The thermodynamic definition of entropy was developed in 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 char... | https://en.wikipedia.org/wiki?curid=9891 |
17,308 | While Clausius based his definition on a reversible process, there are also irreversible processes that change entropy. Following the second law of thermodynamics, entropy of an isolated system always increases for irreversible processes. The difference between an isolated system and closed system is that energy may "n... | https://en.wikipedia.org/wiki?curid=9891 |
17,309 | According to the Clausius equality, for a reversible cyclic process: formula_15. This means the line integral formula_16 is path-independent. | https://en.wikipedia.org/wiki?curid=9891 |
17,310 | To find the entropy difference between any two states of a system, the integral must be evaluated for some reversible path between the initial and final states. Since entropy is a state function, the entropy change of the system for an irreversible path is the same as for a reversible path between the same two states. ... | https://en.wikipedia.org/wiki?curid=9891 |
17,311 | We can only obtain the change of entropy by integrating the above formula. To obtain the absolute value of the entropy, we need the third law of thermodynamics, which states that "S" = 0 at absolute zero for perfect crystals. | https://en.wikipedia.org/wiki?curid=9891 |
17,312 | From a macroscopic perspective, in classical thermodynamics the entropy is interpreted as a state function of a thermodynamic system: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. In any process where the system gives up energy Δ"E", and its en... | https://en.wikipedia.org/wiki?curid=9891 |
17,313 | The statistical definition was developed by Ludwig Boltzmann in the 1870s by analyzing the statistical behavior 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,... | https://en.wikipedia.org/wiki?curid=9891 |
17,314 | The interpretation of entropy in statistical mechanics is the measure of uncertainty, disorder, or "mixedupness" in the phrase of Gibbs, which remains about a system after its observable macroscopic properties, such as temperature, pressure and volume, have been taken into account. For a given set of macroscopic variab... | https://en.wikipedia.org/wiki?curid=9891 |
17,315 | The Boltzmann constant, and therefore entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin (J⋅K) in the International System of Units (or kg⋅m⋅s⋅K in terms of base units). The entropy of a substance is usually given as an intensive propertyeither entropy per unit mass (SI uni... | https://en.wikipedia.org/wiki?curid=9891 |
17,316 | Specifically, entropy is a logarithmic measure of the number of system states with significant probability of being occupied: | https://en.wikipedia.org/wiki?curid=9891 |
17,317 | (formula_19 is the probability that the system is in formula_20th state, usually given by the Boltzmann distribution; if states are defined in a continuous manner, the summation is replaced by an integral over all possible states) or, equivalently, the expected value of the logarithm of the probability that a microstat... | https://en.wikipedia.org/wiki?curid=9891 |
17,318 | The summation is over all the possible microstates of the system, and "p" is the probability that the system is in the "i"-th microstate. This definition assumes that the basis set of states has been picked so that there is no information on their relative phases. In a different basis set, the more general expression i... | https://en.wikipedia.org/wiki?curid=9891 |
17,319 | where formula_23 is the density matrix, formula_24 is trace and formula_25 is the matrix logarithm. This density matrix formulation is not needed in cases of thermal equilibrium so long as the basis states are chosen to be energy eigenstates. For most practical purposes, this can be taken as the fundamental definition ... | https://en.wikipedia.org/wiki?curid=9891 |
17,320 | In what has been called "the fundamental assumption of statistical thermodynamics" or "the fundamental postulate in statistical mechanics", among system microstates of the same energy (degenerate microstates) each microstate is assumed to be populated with equal probability; this assumption is usually justified for an ... | https://en.wikipedia.org/wiki?curid=9891 |
17,321 | In thermodynamics, such a system is one in which the volume, number of molecules, and internal energy are fixed (the microcanonical ensemble). | https://en.wikipedia.org/wiki?curid=9891 |
17,322 | For a given thermodynamic system, the "excess entropy" is defined as the entropy minus that of an ideal gas at the same density and temperature, a quantity that is always negative because an ideal gas is maximally disordered. This concept plays an important role in liquid-state theory. For instance, Rosenfeld's excess-... | https://en.wikipedia.org/wiki?curid=9891 |
17,323 | The most general interpretation of entropy is as a measure of the extent of uncertainty about a system. The equilibrium state of a system maximizes the entropy because it does not reflect all information about the initial conditions, except for the conserved variables. This uncertainty is not of the everyday subjective... | https://en.wikipedia.org/wiki?curid=9891 |
17,324 | The interpretative model has a central role in determining entropy. The qualifier "for a given set of macroscopic variables" above has deep implications: if two observers use different sets of macroscopic variables, they see different entropies. For example, if observer A uses the variables "U", "V" and "W", and observ... | https://en.wikipedia.org/wiki?curid=9891 |
17,325 | Entropy can be defined for any Markov processes with reversible dynamics and the detailed balance property. | https://en.wikipedia.org/wiki?curid=9891 |
17,326 | In Boltzmann's 1896 "Lectures on Gas Theory", he showed that this expression gives a measure of entropy for systems of atoms and molecules in the gas phase, thus providing a measure for the entropy of classical thermodynamics. | https://en.wikipedia.org/wiki?curid=9891 |
17,327 | Entropy arises directly from the Carnot cycle. It can also be described as the reversible heat divided by temperature. Entropy is a fundamental function of state. | https://en.wikipedia.org/wiki?curid=9891 |
17,328 | In a thermodynamic system, pressure and temperature tend to become uniform over time because the equilibrium state has higher probability (more possible combinations of microstates) than any other state. | https://en.wikipedia.org/wiki?curid=9891 |
17,329 | As an example, for a glass of ice water in air at room temperature, the difference in temperature between the warm room (the surroundings) and the cold glass of ice and water (the system and not part of the room) decreases as portions of the thermal energy from the warm surroundings spread to the cooler system of ice a... | https://en.wikipedia.org/wiki?curid=9891 |
17,330 | However, as calculated in the example, the entropy of the system of ice and water has increased more than the entropy of the surrounding room has decreased. In an isolated system such as the room and ice water taken together, the dispersal of energy from warmer to cooler always results in a net increase in entropy. Thu... | https://en.wikipedia.org/wiki?curid=9891 |
17,331 | 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 spontaneously while their time reversals (also permitted by conservation laws) d... | https://en.wikipedia.org/wiki?curid=9891 |
17,332 | Unlike many other functions of state, entropy cannot be directly observed but must be calculated. Absolute standard molar entropy of a substance can be calculated from the measured temperature dependence of its heat capacity. The molar entropy of ions is obtained as a difference in entropy from a reference state define... | https://en.wikipedia.org/wiki?curid=9891 |
17,333 | One dictionary definition of entropy is that it is "a measure of thermal energy per unit temperature that is not available for useful work" in a cyclic process. For instance, a substance at uniform temperature is at maximum entropy and cannot drive a heat engine. A substance at non-uniform temperature is at a lower ent... | https://en.wikipedia.org/wiki?curid=9891 |
17,334 | A special case of entropy increase, the entropy of mixing, occurs when two or more different substances are mixed. If the substances are at the same temperature and pressure, there is no net exchange of heat or work – the entropy change is entirely due to the mixing of the different substances. At a statistical mechani... | https://en.wikipedia.org/wiki?curid=9891 |
17,335 | Proofs of equivalence between the definition of entropy in statistical mechanics (the Gibbs entropy formula formula_27) and in classical thermodynamics (formula_5 together with the fundamental thermodynamic relation) are known for the microcanonical ensemble, the canonical ensemble, the grand canonical ensemble, and th... | https://en.wikipedia.org/wiki?curid=9891 |
17,336 | Furthermore, it has been shown that the definitions of entropy in statistical mechanics is the only entropy that is equivalent to the classical thermodynamics entropy under the following postulates: | https://en.wikipedia.org/wiki?curid=9891 |
17,337 | 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 not to decrease. It follows that heat cannot flow from a colder body... | https://en.wikipedia.org/wiki?curid=9891 |
17,338 | It follows from the second law of thermodynamics that the entropy of a system that is not isolated may decrease. An air conditioner, for example, may cool the air in a room, thus reducing the entropy of the air of that system. The heat expelled from the room (the system), which the air conditioner transports and discha... | https://en.wikipedia.org/wiki?curid=9891 |
17,339 | In mechanics, the second law in conjunction with the fundamental thermodynamic relation places limits on a system's ability to do useful work. The entropy change of a system at temperature formula_4 absorbing an infinitesimal amount of heat formula_31 in a reversible way, is given by formula_32. More explicitly, an ene... | https://en.wikipedia.org/wiki?curid=9891 |
17,340 | Statistical mechanics demonstrates that entropy is governed by probability, thus allowing for a decrease in disorder even in an isolated system. Although this is possible, such an event has a small probability of occurring, making it unlikely. | https://en.wikipedia.org/wiki?curid=9891 |
17,341 | The applicability of a second law of thermodynamics is limited to systems in or sufficiently near equilibrium state, so that they have defined entropy. Some inhomogeneous systems out of thermodynamic equilibrium still satisfy the hypothesis of local thermodynamic equilibrium, so that entropy density is locally defined ... | https://en.wikipedia.org/wiki?curid=9891 |
17,342 | The entropy of a system depends on its internal energy and its external parameters, such as its volume. In the thermodynamic limit, this fact leads to an equation relating the change in the internal energy formula_1 to changes in the entropy and the external parameters. This relation is known as the "fundamental thermo... | https://en.wikipedia.org/wiki?curid=9891 |
17,343 | Since both internal energy and entropy are monotonic functions of temperature formula_39, implying that the internal energy is fixed when one specifies the entropy and the volume, this relation is valid even if the change from one state of thermal equilibrium to another with infinitesimally larger entropy and volume ha... | https://en.wikipedia.org/wiki?curid=9891 |
17,344 | The fundamental thermodynamic relation implies many thermodynamic identities that are valid in general, independent of the microscopic details of the system. Important examples are the Maxwell relations and the relations between heat capacities. | https://en.wikipedia.org/wiki?curid=9891 |
17,345 | Thermodynamic entropy is central in chemical thermodynamics, enabling changes to be quantified and the outcome of reactions predicted. The second law of thermodynamics states that entropy in an isolated system – the combination of a subsystem under study and its surroundings – increases during all spontaneous chemical ... | https://en.wikipedia.org/wiki?curid=9891 |
17,346 | The thermodynamic entropy therefore has the dimension of energy divided by temperature, and the unit joule per kelvin (J/K) in the International System of Units (SI). | https://en.wikipedia.org/wiki?curid=9891 |
17,347 | Thermodynamic entropy is an extensive property, meaning that it scales with the size or extent of a system. In many processes it is useful to specify the entropy as an intensive property independent of the size, as a specific entropy characteristic of the type of system studied. Specific entropy may be expressed relati... | https://en.wikipedia.org/wiki?curid=9891 |
17,348 | Thus, when one mole of substance at about is warmed by its surroundings to , the sum of the incremental values of formula_42 constitute each element's or compound's standard molar entropy, an indicator of the amount of energy stored by a substance at . Entropy change also measures the mixing of substances as a summatio... | https://en.wikipedia.org/wiki?curid=9891 |
17,349 | Entropy is equally essential in predicting the extent and direction of complex chemical reactions. For such applications, formula_41 must be incorporated in an expression that includes both the system and its surroundings, formula_44. This expression becomes, via some steps, the Gibbs free energy equation for reactants... | https://en.wikipedia.org/wiki?curid=9891 |
17,350 | A 2011 study in Science (journal) estimated the world's technological capacity to store and communicate optimally compressed information normalized on the most effective compression algorithms available in the year 2007, therefore estimating the entropy of the technologically available sources. The author's estimate th... | https://en.wikipedia.org/wiki?curid=9891 |
17,351 | In chemical engineering, the principles of thermodynamics are commonly applied to "open systems", i.e. those in which heat, work, and mass flow across the system boundary. Flows of both heat (formula_48) and work, i.e. formula_49 (shaft work) and formula_50 (pressure-volume work), across the system boundaries, in gener... | https://en.wikipedia.org/wiki?curid=9891 |
17,352 | To derive a generalized entropy balanced equation, we start with the general balance equation for the change in any extensive quantity formula_53 in a thermodynamic system, a quantity that may be either conserved, such as energy, or non-conserved, such as entropy. The basic generic balance expression states that formul... | https://en.wikipedia.org/wiki?curid=9891 |
17,353 | If there are multiple heat flows, the term formula_51 is replaced by formula_67 where formula_68 is the heat flow and formula_69 is the temperature at the formula_70th heat flow port into the system. | https://en.wikipedia.org/wiki?curid=9891 |
17,354 | Note that the nomenclature "entropy balance" is misleading and often deemed inappropriate because entropy is not a conserved quantity. In other words, the term formula_71 is never a known quantity but always a derived one based on the expression above. Therefore, the open system version of the second law is more approp... | https://en.wikipedia.org/wiki?curid=9891 |
17,355 | For certain simple transformations in systems of constant composition, the entropy changes are given by simple formulas. | https://en.wikipedia.org/wiki?curid=9891 |
17,356 | For the expansion (or compression) of an ideal gas from an initial volume formula_73 and pressure formula_74 to a final volume formula_37 and pressure formula_76 at any constant temperature, the change in entropy is given by: | https://en.wikipedia.org/wiki?curid=9891 |
17,357 | Here formula_78 is the amount of gas (in moles) and formula_79 is the ideal gas constant. These equations also apply for expansion into a finite vacuum or a throttling process, where the temperature, internal energy and enthalpy for an ideal gas remain constant. | https://en.wikipedia.org/wiki?curid=9891 |
17,358 | For pure heating or cooling of any system (gas, liquid or solid) at constant pressure from an initial temperature formula_80 to a final temperature formula_39, the entropy change is | https://en.wikipedia.org/wiki?curid=9891 |
17,359 | provided that the constant-pressure molar heat capacity (or specific heat) "C" is constant and that no phase transition occurs in this temperature interval. | https://en.wikipedia.org/wiki?curid=9891 |
17,360 | At low temperatures near absolute zero, heat capacities of solids quickly drop off to near zero, so the assumption of constant heat capacity does not apply. | https://en.wikipedia.org/wiki?curid=9891 |
17,361 | Since entropy is 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 | https://en.wikipedia.org/wiki?curid=9891 |
17,362 | Reversible phase transitions occur at constant temperature and pressure. The reversible heat is the enthalpy change for the transition, and the entropy change is the enthalpy change divided by the thermodynamic temperature. For fusion (melting) of a solid to a liquid at the melting point "T", the entropy of fusion is | https://en.wikipedia.org/wiki?curid=9891 |
17,363 | Similarly, for vaporization of a liquid to a gas at the boiling point "T", the entropy of vaporization is | https://en.wikipedia.org/wiki?curid=9891 |
17,364 | As a fundamental aspect of thermodynamics and physics, several different approaches to entropy beyond that of Clausius and Boltzmann are valid. | https://en.wikipedia.org/wiki?curid=9891 |
17,365 | In Boltzmann's analysis in terms of constituent particles, entropy is a measure of the number of possible microscopic states (or microstates) of a system in thermodynamic equilibrium. | https://en.wikipedia.org/wiki?curid=9891 |
17,366 | Entropy is often loosely associated with the amount of order or disorder, or of chaos, in a thermodynamic system. The traditional qualitative description of entropy is that it refers to changes in the status quo of the system and is a measure of "molecular disorder" and the amount of wasted energy in a dynamical energy... | https://en.wikipedia.org/wiki?curid=9891 |
17,367 | In which "C" is the "disorder" capacity of the system, which is the entropy of the parts contained in the permitted ensemble, "C" is the "information" capacity of the system, an expression similar to Shannon's channel capacity, and "C" is the "order" capacity of the system. | https://en.wikipedia.org/wiki?curid=9891 |
17,368 | 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 early in the history of classical thermodynamics, and with the development of statistical thermodynamics and quantum theory, entropy changes have been described in terms ... | https://en.wikipedia.org/wiki?curid=9891 |
17,369 | Ambiguities in the terms "disorder" and "chaos", which usually have meanings directly opposed to equilibrium, contribute to widespread confusion and hamper comprehension of entropy for most students. As the second law of thermodynamics shows, in an isolated system internal portions at different temperatures tend to adj... | https://en.wikipedia.org/wiki?curid=9891 |
17,370 | It is possible (in a thermal context) to regard lower entropy as a measure of the "effectiveness" or "usefulness" of a particular quantity of energy. Energy supplied at a higher temperature (i.e. with low entropy) tends to be more useful than the same amount of energy available at a lower temperature. Mixing a hot parc... | https://en.wikipedia.org/wiki?curid=9891 |
17,371 | As the entropy of the universe is steadily increasing, its total energy is becoming less useful. Eventually, this leads to the heat death of the universe. | https://en.wikipedia.org/wiki?curid=9891 |
17,372 | A definition of entropy based entirely on the relation of adiabatic accessibility between equilibrium states was given by E.H.Lieb and J. Yngvason in 1999. This approach has several predecessors, including the pioneering work of Constantin Carathéodory from 1909 and the monograph by R. Giles. In the setting of Lieb and... | https://en.wikipedia.org/wiki?curid=9891 |
17,373 | In quantum statistical mechanics, the concept of entropy was developed by John von Neumann and is generally referred to as "von Neumann entropy", | https://en.wikipedia.org/wiki?curid=9891 |
17,374 | This upholds the correspondence principle, because in the classical limit, when the phases between the basis states used for the classical probabilities are purely random, this expression is equivalent to the familiar classical definition of entropy, | https://en.wikipedia.org/wiki?curid=9891 |
17,375 | Von Neumann established a rigorous mathematical framework for quantum mechanics with his work "Mathematische Grundlagen der Quantenmechanik". He provided in this work a theory of measurement, where the usual notion of wave function collapse is described as an irreversible process (the so-called von Neumann or projectiv... | https://en.wikipedia.org/wiki?curid=9891 |
17,376 | When viewed in terms of information theory, the entropy state function is the amount of information in the system that is needed to fully specify the microstate of the system. Entropy is the measure of the amount of missing information before reception. Often called "Shannon entropy", it was originally devised by Claud... | https://en.wikipedia.org/wiki?curid=9891 |
17,377 | In the case of transmitted messages, these probabilities were the probabilities that a particular message was actually transmitted, and the entropy of the message system was a measure of the average size of information of a message. For the case of equal probabilities (i.e. each message is equally probable), the Shanno... | https://en.wikipedia.org/wiki?curid=9891 |
17,378 | Most researchers consider information entropy and thermodynamic entropy directly linked to the same concept, while others argue that they are distinct. Both expressions are mathematically similar. If formula_6 is the number of microstates that can yield a given macrostate, and each microstate has the same "a priori" pr... | https://en.wikipedia.org/wiki?curid=9891 |
17,379 | which is the Boltzmann entropy formula, where formula_106 is the Boltzmann constant, which may be interpreted as the thermodynamic entropy per nat. Some authors argue for dropping the word entropy for the formula_109 function of information theory and using Shannon's other term, "uncertainty", instead. | https://en.wikipedia.org/wiki?curid=9891 |
17,380 | The entropy of a substance can be measured, although in an indirect way. The measurement, known as entropymetry, is done on a closed system (with particle number N and volume V being constants) and uses the definition of temperature in terms of entropy, while limiting energy exchange to heat (formula_110). | https://en.wikipedia.org/wiki?curid=9891 |
17,381 | The resulting relation describes how entropy changes formula_112 when a small amount of energy formula_113 is introduced into the system at a certain temperature formula_39. | https://en.wikipedia.org/wiki?curid=9891 |
17,382 | The process of measurement goes as follows. First, a sample of the substance is cooled as close to absolute zero as possible. At such temperatures, the entropy approaches zerodue to the definition of temperature. Then, small amounts of heat are introduced into the sample and the change in temperature is recorded, until... | https://en.wikipedia.org/wiki?curid=9891 |
17,383 | Although the concept of entropy was originally a thermodynamic concept, it has been adapted in other fields of study, including information theory, psychodynamics, thermoeconomics/ecological economics, and evolution. | https://en.wikipedia.org/wiki?curid=9891 |
17,384 | Entropy is the only quantity in the physical sciences that seems to imply a particular direction of progress, sometimes called an arrow of time. As time progresses, the second law of thermodynamics states that the entropy of an isolated system never decreases in large systems over significant periods of time. Hence, fr... | https://en.wikipedia.org/wiki?curid=9891 |
17,385 | Chiavazzo "et al." proposed that where cave spiders choose to lay their eggs can be explained through entropy minimization. | https://en.wikipedia.org/wiki?curid=9891 |
17,386 | Entropy has been proven useful in the analysis of base pair sequences in DNA. Many entropy-based measures have been shown to distinguish between different structural regions of the genome, differentiate between coding and non-coding regions of DNA, and can also be applied for the recreation of evolutionary trees by det... | https://en.wikipedia.org/wiki?curid=9891 |
17,387 | Assuming that a finite universe is an isolated system, the second law of thermodynamics states that its total entropy is continually increasing. It has been speculated, since the 19th century, that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy so t... | https://en.wikipedia.org/wiki?curid=9891 |
17,388 | If the universe can be considered to have generally increasing entropy, then – as Roger Penrose has pointed out – gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. The entropy of a black hole is proportional to t... | https://en.wikipedia.org/wiki?curid=9891 |
17,389 | 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 hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the ... | https://en.wikipedia.org/wiki?curid=9891 |
17,390 | Current theories suggest the entropy gap to have been originally opened up by the early rapid exponential expansion of the universe. | https://en.wikipedia.org/wiki?curid=9891 |
17,391 | Romanian American economist Nicholas Georgescu-Roegen, a progenitor in economics and a paradigm founder of ecological economics, made extensive use of the entropy concept in his magnum opus on "The Entropy Law and the Economic Process". Due to Georgescu-Roegen's work, the laws of thermodynamics form an integral part of... | https://en.wikipedia.org/wiki?curid=9891 |
17,392 | In economics, Georgescu-Roegen's work has generated the term 'entropy pessimism'. Since the 1990s, leading ecological economist and steady-state theorist Herman Daly – a student of Georgescu-Roegen – has been the economics profession's most influential proponent of the entropy pessimism position. | https://en.wikipedia.org/wiki?curid=9891 |
17,393 | Methylphenidate, sold under the brand names Ritalin and Concerta among others, is the most widely prescribed central nervous system (CNS) stimulant medication used to treat attention deficit hyperactivity disorder (ADHD) and, to a lesser extent, narcolepsy. It is a primary medication for ADHD; it may be taken by mouth ... | https://en.wikipedia.org/wiki?curid=205878 |
17,394 | Common adverse reactions of methylphenidate include: tachycardia, palpitations, headache, insomnia, anxiety, hyperhidrosis, weight loss, decreased appetite, dry mouth, nausea, and abdominal pain. Withdrawal symptoms may include: chills, depression, drowsiness, dysphoria, exhaustion, headaches, irritability, lethargy, n... | https://en.wikipedia.org/wiki?curid=205878 |
17,395 | Methylphenidate is believed to work by blocking the reuptake of dopamine and norepinephrine by neurons. It is a central nervous system (CNS) stimulant of the phenethylamine and piperidine classes. Despite the claim made by some urban legends, it is not a cocaine derivative nor analog; cocaine is a local anesthetic and ... | https://en.wikipedia.org/wiki?curid=205878 |
17,396 | Methylphenidate was first synthesized in 1944 and was approved for medical use in the United States in 1955. It was originally sold by Swiss company CIBA (now Novartis). It was estimated that the number of doses of methylphenidate used globally in 2013 increased by 66% compared to 2012. In 2020, it was the 41st most co... | https://en.wikipedia.org/wiki?curid=205878 |
17,397 | In the United Kingdom, through the National Health Service, the drug is first-line medication for the treatment of attention deficit hyperactivity disorder (ADHD). | https://en.wikipedia.org/wiki?curid=205878 |
17,398 | Methylphenidate is used for the treatment of attention deficit hyperactivity disorder. The addition of behavioural modification therapy can have additional benefits on treatment outcome. The dosage may vary and is titrated to effect, with some guidelines recommending initial treatment with a low dose. Immediate release... | https://en.wikipedia.org/wiki?curid=205878 |
17,399 | In children over age 6 and adolescents, the short-term benefits and cost effectiveness of methylphenidate are well established. A number of reviews have established the safety and effectiveness for individuals with ADHD over several years. | https://en.wikipedia.org/wiki?curid=205878 |
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