101-424: Entropia may mean: Entropy a scientific concept that is most commonly associated with a state of disorder, randomness, or uncertainty. Entropia Universe (formerly known as Project Entropia), a popular MMORPG-style online virtual universe. Entropia, Inc. (company) , a defunct company that produced commercial distributed computing software. Entropia (album) ,
202-417: 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. 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
303-529: A Greek mathematician, linked entropy with a mathematical definition of irreversibility, in terms of trajectories and integrability. In 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 ) as
404-470: A case where the "feed-back" action is positive in contrast to negative feed-back action, which they mentioned only in passing. Harold Stephen Black 's classic 1934 paper first details the use of negative feedback in electronic amplifiers. According to Black: Positive feed-back increases the gain of the amplifier, negative feed-back reduces it. According to Mindell (2002) confusion in the terms arose shortly after this: ... Friis and Jensen had made
505-695: A central concept for the first law of thermodynamics . Finally, a comparison of both the representations of a work output in a Carnot cycle gives us: | Q H | T H − | Q C | T C = Q H T H + Q C T C = 0 {\displaystyle {\frac {\left\vert Q_{\mathsf {H}}\right\vert }{T_{\mathsf {H}}}}-{\frac {\left\vert Q_{\mathsf {C}}\right\vert }{T_{\mathsf {C}}}}={\frac {Q_{\mathsf {H}}}{T_{\mathsf {H}}}}+{\frac {Q_{\mathsf {C}}}{T_{\mathsf {C}}}}=0} Similarly to
606-493: A circular argument. This makes reasoning based upon cause and effect tricky, and it is necessary to analyze the system as a whole. As provided by Webster, feedback in business is the transmission of evaluative or corrective information about an action, event, or process to the original or controlling source. Self-regulating mechanisms have existed since antiquity, and the idea of feedback started to enter economic theory in Britain by
707-482: A classic in feedback control theory. This was a landmark paper on control theory and the mathematics of feedback. The verb phrase to feed back , in the sense of returning to an earlier position in a mechanical process, was in use in the US by the 1860s, and in 1909, Nobel laureate Karl Ferdinand Braun used the term "feed-back" as a noun to refer to (undesired) coupling between components of an electronic circuit . By
808-529: A cold one. If we consider a heat engine which is less effective than Carnot cycle (i.e., the work W {\textstyle W} produced by this engine is less than the maximum predicted by Carnot's theorem), its work output is capped by Carnot efficiency as: W < ( 1 − T C T H ) Q H {\displaystyle W<\left(1-{\frac {T_{\mathsf {C}}}{T_{\mathsf {H}}}}\right)Q_{\mathsf {H}}} Substitution of
909-434: A deliberate effect via some more tangible connection. [Practical experimenters] object to the mathematician's definition, pointing out that this would force them to say that feedback was present in the ordinary pendulum ... between its position and its momentum—a "feedback" that, from the practical point of view, is somewhat mystical. To this the mathematician retorts that if feedback is to be considered present only when there
1010-451: A gas, and later quantum-mechanically (photons, phonons , spins, etc.). The two approaches form a consistent, unified view of the same phenomenon as expressed in the second law of thermodynamics, which has found universal applicability to physical processes. Many thermodynamic properties are defined by physical variables that define a state of thermodynamic equilibrium , which essentially are state variables . State variables depend only on
1111-470: A given quantity of gas determine its state, and thus also its volume via the ideal gas law . A system composed of a pure substance of a single phase at a particular uniform temperature and pressure is determined, and is thus a particular state, and has a particular volume. The fact that entropy is a function of state makes it useful. In the Carnot cycle , the working fluid returns to the same state that it had at
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#17329207542931212-676: 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 Δ E {\displaystyle \Delta E} of energy to the surrounding at the temperature T {\textstyle T} , its entropy falls by Δ S {\textstyle \Delta S} and at least T ⋅ Δ S {\textstyle T\cdot \Delta S} of that energy must be given up to
1313-533: A music album by the Swedish progressive metal band, Pain of Salvation. Entropa , a satirical art installation depicting member countries of the European Union See also [ edit ] Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Entropia . If an internal link led you here, you may wish to change the link to point directly to
1414-419: A nutrient elicits changes in some of their metabolic functions. Feedback is also central to the operations of genes and gene regulatory networks . Repressor (see Lac repressor ) and activator proteins are used to create genetic operons , which were identified by François Jacob and Jacques Monod in 1961 as feedback loops . These feedback loops may be positive (as in the case of the coupling between
1515-582: A process, whereas the positive feedback loop tends to accelerate it. The mirror neurons are part of a social feedback system, when an observed action is "mirrored" by the brain—like a self-performed action. Normal tissue integrity is preserved by feedback interactions between diverse cell types mediated by adhesion molecules and secreted molecules that act as mediators; failure of key feedback mechanisms in cancer disrupts tissue function. In an injured or infected tissue, inflammatory mediators elicit feedback responses in cells, which alter gene expression, and change
1616-440: A reversible path between the same two states. However, the heat transferred to or from the surroundings is different as well as its entropy change. We can calculate the change of entropy only by integrating the above formula. To obtain the absolute value of the entropy, we consider the third law of thermodynamics : perfect crystals at the absolute zero have an entropy S = 0 {\textstyle S=0} . From
1717-524: A single discipline an example of feedback can be called either positive or negative, depending on how values are measured or referenced. This confusion may arise because feedback can be used to provide information or motivate , and often has both a qualitative and a quantitative component. As Connellan and Zemke (1993) put it: Quantitative feedback tells us how much and how many. Qualitative feedback tells us how good, bad or indifferent. While simple systems can sometimes be described as one or
1818-481: A sugar molecule and the proteins that import sugar into a bacterial cell), or negative (as is often the case in metabolic consumption). On a larger scale, feedback can have a stabilizing effect on animal populations even when profoundly affected by external changes, although time lags in feedback response can give rise to predator-prey cycles . In zymology , feedback serves as regulation of activity of an enzyme by its direct product(s) or downstream metabolite(s) in
1919-418: A system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems: Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to
2020-430: A violation of the second law of thermodynamics, since he does not possess information about variable X {\textstyle X} and its influence on the system. In other words, one must choose a complete 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
2121-414: A word that meant the same thing to everybody: nothing". Any method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension. The concept of entropy is described by two principal approaches, the macroscopic perspective of classical thermodynamics , and
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#17329207542932222-407: Is a density matrix , t r {\displaystyle \mathrm {tr} } is a trace operator and ln {\displaystyle \ln } is a matrix logarithm . Density matrix formalism is not required if the system occurs to be in a thermal equilibrium so long as the basis states are chosen to be eigenstates of Hamiltonian . For most practical purposes it can be taken as
2323-557: Is a logarithmic measure for the system with a number of states, each with a probability p i {\textstyle p_{i}} of being occupied (usually given by the Boltzmann distribution ): S = − k B ∑ i p i ln p i {\displaystyle S=-k_{\mathsf {B}}\sum _{i}{p_{i}\ln {p_{i}}}} where k B {\textstyle k_{\mathsf {B}}}
2424-576: Is a scientific concept that is most commonly associated with a state 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 information theory . It has found far-ranging applications in chemistry and physics , in biological systems and their relation to life, in cosmology , economics , sociology , weather science , climate change , and information systems including
2525-456: Is a temperature difference between reservoirs. Originally, Carnot did not distinguish between heats Q H {\textstyle Q_{\mathsf {H}}} and Q C {\textstyle Q_{\mathsf {C}}} , as he assumed caloric theory to be valid and hence that the total heat in the system was conserved. But in fact, the magnitude of heat Q H {\textstyle Q_{\mathsf {H}}}
2626-399: Is also found in certain behaviour. For example, "shame loops" occur in people who blush easily. When they realize that they are blushing, they become even more embarrassed, which leads to further blushing, and so on. The climate system is characterized by strong positive and negative feedback loops between processes that affect the state of the atmosphere, ocean, and land. A simple example is
2727-461: Is an actual wire or nerve to represent it, then the theory becomes chaotic and riddled with irrelevancies. Focusing on uses in management theory, Ramaprasad (1983) defines feedback generally as "...information about the gap between the actual level and the reference level of a system parameter" that is used to "alter the gap in some way". He emphasizes that the information by itself is not feedback unless translated into action. Positive feedback: If
2828-448: 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 efficiency (i.e., the efficiency of all reversible heat engines with the same pair of thermal reservoirs) and
2929-414: Is known that a work W > 0 {\textstyle W>0} produced by an engine over a cycle equals to a net heat Q Σ = | Q H | − | Q C | {\textstyle Q_{\Sigma }=\left\vert Q_{\mathsf {H}}\right\vert -\left\vert Q_{\mathsf {C}}\right\vert } absorbed over a cycle. Thus, with
3030-510: Is now known as heat) falls through a temperature difference, work or motive power can be produced from the actions of its fall from a hot to cold body. He used an analogy with how water falls in a water wheel . That was an early insight into the second law of thermodynamics . Carnot based his views of heat partially on the early 18th-century "Newtonian hypothesis" that both heat and light were types of indestructible forms of matter, which are attracted and repelled by other matter, and partially on
3131-406: Is one with a fixed volume, number of molecules, and internal energy, called a microcanonical ensemble . 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
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3232-571: Is that energy may not flow to and from an isolated system, but energy flow to and from a closed system is possible. Nevertheless, for both closed and isolated systems, and indeed, also in open systems, irreversible thermodynamics processes may occur. According to the Clausius equality , for a reversible cyclic thermodynamic process: ∮ δ Q r e v T = 0 {\displaystyle \oint {\frac {\delta Q_{\mathsf {rev}}}{T}}=0} which means
3333-567: Is the Boltzmann constant and the summation is performed over all possible microstates of the system. In case states are defined in a continuous manner, the summation is replaced by an integral over all possible states, or equivalently we can consider the expected value of the logarithm of the probability that a microstate is occupied: S = − k B ⟨ ln p ⟩ {\displaystyle S=-k_{\mathsf {B}}\left\langle \ln {p}\right\rangle } This definition assumes
3434-453: Is the car; its input includes the combined torque from the engine and from the changing slope of the road (the disturbance). The car's speed (status) is measured by a speedometer . The error signal is the difference of the speed as measured by the speedometer from the target speed (set point). The controller interprets the speed to adjust the accelerator, commanding the fuel flow to the engine (the effector). The resulting change in engine torque,
3535-405: Is the number of microstates whose energy equals to the one of the system. Usually, this assumption is justified for an isolated system in a thermodynamic equilibrium. Then in case of an isolated system the previous formula reduces to: S = k B ln Ω {\displaystyle S=k_{\mathsf {B}}\ln {\Omega }} In thermodynamics, such a system
3636-512: Is used to boost poor performance (narrow a gap). Referring to definition 1, some authors use alternative terms, replacing positive and negative with self-reinforcing and self-correcting , reinforcing and balancing , discrepancy-enhancing and discrepancy-reducing or regenerative and degenerative respectively. And for definition 2, some authors promote describing the action or effect as positive and negative reinforcement or punishment rather than feedback. Yet even within
3737-566: Is zero too, since the inversion of a heat transfer direction means a sign inversion for the heat transferred during isothermal stages: − Q H T H − Q C T C = Δ S r , H + Δ S r , C = 0 {\displaystyle -{\frac {Q_{\mathsf {H}}}{T_{\mathsf {H}}}}-{\frac {Q_{\mathsf {C}}}{T_{\mathsf {C}}}}=\Delta S_{\mathsf {r,H}}+\Delta S_{\mathsf {r,C}}=0} Here we denote
3838-411: The Carnot cycle which is a thermodynamic cycle performed by a Carnot heat engine as a reversible heat engine. In a Carnot cycle the heat Q H {\textstyle Q_{\mathsf {H}}} is transferred from a hot reservoir to a working gas at the constant temperature T H {\textstyle T_{\mathsf {H}}} during isothermal expansion stage and
3939-417: The biosphere , most parameters must stay under control within a narrow range around a certain optimal level under certain environmental conditions. The deviation of the optimal value of the controlled parameter can result from the changes in internal and external environments. A change of some of the environmental conditions may also require change of that range to change for the system to function. The value of
4040-403: The centrifugal governors used in steam engines. He distinguished those that lead to a continued increase in a disturbance or the amplitude of a wave or oscillation, from those that lead to a decrease of the same quality. The terms positive and negative feedback are defined in different ways within different disciplines. The two definitions may be confusing, like when an incentive (reward)
4141-433: The detailed balance property. 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. 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. In
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4242-401: The steam engines of their production. Early steam engines employed a purely reciprocating motion , and were used for pumping water – an application that could tolerate variations in the working speed, but the use of steam engines for other applications called for more precise control of the speed. In 1868 , James Clerk Maxwell wrote a famous paper, "On governors", that is widely considered
4343-455: The 18th century, but it was not at that time recognized as a universal abstraction and so did not have a name. The first ever known artificial feedback device was a float valve , for maintaining water at a constant level, invented in 270 BC in Alexandria , Egypt . This device illustrated the principle of feedback: a low water level opens the valve, the rising water then provides feedback into
4444-445: The 1940s onwards was centred around the study of circular causal feedback mechanisms. Over the years there has been some dispute as to the best definition of feedback. According to cybernetician Ashby (1956), mathematicians and theorists interested in the principles of feedback mechanisms prefer the definition of "circularity of action", which keeps the theory simple and consistent. For those with more practical aims, feedback should be
4545-527: The Carnot efficiency Kelvin had to evaluate the ratio of the work output to the heat absorbed during the isothermal expansion with the help of the Carnot–Clapeyron equation, which contained an unknown function called the Carnot function. The possibility that the Carnot function could be the temperature as measured from a zero point of temperature was suggested by Joule in a letter to Kelvin. This allowed Kelvin to establish his absolute temperature scale. It
4646-547: The French mathematician Lazare Carnot proposed that in any machine, the accelerations and shocks of the moving parts represent losses of moment of activity ; in any natural process there exists an inherent tendency towards the dissipation of useful energy. In 1824, building on that work, Lazare's son, Sadi Carnot , published Reflections on the Motive Power of Fire , which posited that in all heat-engines, whenever " caloric " (what
4747-541: The basis states to be picked in a way that there is no information on their relative phases. In a general case the expression is: 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 }}}
4848-410: The concept, providing an explanation and a deeper understanding of its nature. 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 variables,
4949-403: The contemporary views of Count Rumford , who showed in 1789 that heat could be created by friction, as when cannon bores are machined. Carnot reasoned that if the body of the working substance, such as a body of steam, is returned to its original state at the end of a complete engine cycle , "no change occurs in the condition of the working body". The first law of thermodynamics , deduced from
5050-443: The current state and inputs are used to calculate a new state which is then fed back and clocked back into the device to update it. By using feedback properties, the behavior of a system can be altered to meet the needs of an application; systems can be made stable, responsive or held constant. It is shown that dynamical systems with a feedback experience an adaptation to the edge of chaos . Physical systems present feedback through
5151-440: The derivation of internal energy, this equality implies existence of a state function S {\textstyle S} with a change of d S = δ Q / T {\textstyle \mathrm {d} S=\delta Q/T} and which is conserved over an entire cycle. Clausius called this state function entropy . In addition, the total change of entropy in both thermal reservoirs over Carnot cycle
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#17329207542935252-450: The description of devices operating near the limit of de Broglie waves , e.g. photovoltaic cells , have to be consistent with quantum statistics . 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
5353-474: The dimension of 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 entropy change of the system for an irreversible path is the same as for
5454-450: The end of 1912, researchers using early electronic amplifiers ( audions ) had discovered that deliberately coupling part of the output signal back to the input circuit would boost the amplification (through regeneration ), but would also cause the audion to howl or sing. This action of feeding back of the signal from output to input gave rise to the use of the term "feedback" as a distinct word by 1920. The development of cybernetics from
5555-446: The entropy change for a thermal reservoir by Δ 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
5656-409: The entropy measures the degree to which the probability of the system is spread out over different possible microstates . In contrast to the macrostate, which characterizes plainly observable average quantities, a microstate specifies all molecular details about the system including the position and momentum of every molecule. The more such states are available to the system with appreciable probability,
5757-418: The equilibrium condition, not on the path evolution to that state. State variables can be functions of state, also called state functions , in a sense that one state variable is a mathematical function of other state variables. Often, if some properties of a system are determined, they are sufficient to determine the state of the system and thus other properties' values. For example, temperature and pressure of
5858-825: The everyday subjective kind, but rather the uncertainty inherent to the experimental method and interpretative model. The interpretative model has a central role in determining entropy. The qualifier "for a given set of macroscopic variables" above has deep implications when two observers use different sets of macroscopic variables. For example, consider observer A using variables U {\textstyle U} , V {\textstyle V} , W {\textstyle W} and observer B using variables U {\textstyle U} , V {\textstyle V} , W {\textstyle W} , X {\textstyle X} . If observer B changes variable X {\textstyle X} , then observer A will see
5959-405: The feedback, combines with the torque exerted by the change of road grade to reduce the error in speed, minimising the changing slope. The terms "positive" and "negative" were first applied to feedback prior to WWII. The idea of positive feedback already existed in the 1920s when the regenerative circuit was made. Friis and Jensen (1924) described this circuit in a set of electronic amplifiers as
6060-536: The fundamental definition of entropy since all other formulae for S {\textstyle S} can be derived from it, but not vice versa. 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 }
6161-438: The greater the entropy. In statistical mechanics, entropy is a measure of the number of ways a system can be arranged, often taken to be a measure of "disorder" (the higher the entropy, the higher the disorder). This definition describes the entropy as being proportional to the natural logarithm of the number of possible microscopic configurations of the individual atoms and molecules of the system ( microstates ) that could cause
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#17329207542936262-442: The groups of molecules expressed and secreted, including molecules that induce diverse cells to cooperate and restore tissue structure and function. This type of feedback is important because it enables coordination of immune responses and recovery from infections and injuries. During cancer, key elements of this feedback fail. This disrupts tissue function and immunity. Mechanisms of feedback were first elucidated in bacteria, where
6363-437: The heat Q C {\textstyle Q_{\mathsf {C}}} is transferred from a working gas to a cold reservoir at the constant temperature T C {\textstyle T_{\mathsf {C}}} during isothermal compression stage. According to Carnot's theorem , a heat engine with two thermal reservoirs can produce a work W {\textstyle W} if and only if there
6464-605: The heat Q H {\textstyle Q_{\mathsf {H}}} absorbed by a working body of the engine during isothermal expansion: W = T H − T C T H ⋅ Q H = ( 1 − T C T H ) Q H {\displaystyle W={\frac {T_{\mathsf {H}}-T_{\mathsf {C}}}{T_{\mathsf {H}}}}\cdot Q_{\mathsf {H}}=\left(1-{\frac {T_{\mathsf {C}}}{T_{\mathsf {H}}}}\right)Q_{\mathsf {H}}} To derive
6565-434: The heat-friction experiments of James Joule in 1843, expresses the concept of energy and its conservation in all processes; the first law, however, is unsuitable to separately quantify the effects of friction and dissipation . In the 1850s and 1860s, German physicist Rudolf Clausius objected to the supposition that no change occurs in the working body, and gave that change a mathematical interpretation, by questioning
6666-422: The hint that at each stage of the cycle the difference between a work and a net heat would be conserved, rather than a net heat itself. Which means there exists a state function U {\textstyle U} with a change of d U = δ Q − d W {\textstyle \mathrm {d} U=\delta Q-\mathrm {d} W} . It is called an internal energy and forms
6767-1599: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Entropia&oldid=1226253053 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Entropy Collective intelligence Collective action Self-organized criticality Herd mentality Phase transition Agent-based modelling Synchronization Ant colony optimization Particle swarm optimization Swarm behaviour Social network analysis Small-world networks Centrality Motifs Graph theory Scaling Robustness Systems biology Dynamic networks Evolutionary computation Genetic algorithms Genetic programming Artificial life Machine learning Evolutionary developmental biology Artificial intelligence Evolutionary robotics Reaction–diffusion systems Partial differential equations Dissipative structures Percolation Cellular automata Spatial ecology Self-replication Conversation theory Entropy Feedback Goal-oriented Homeostasis Information theory Operationalization Second-order cybernetics Self-reference System dynamics Systems science Systems thinking Sensemaking Variety Ordinary differential equations Phase space Attractors Population dynamics Chaos Multistability Bifurcation Rational choice theory Bounded rationality Entropy
6868-508: The line integral ∫ L δ Q r e v / T {\textstyle \int _{L}{\delta Q_{\mathsf {rev}}/T}} is path-independent . Thus we can define a state function S {\textstyle S} , called entropy : d S = δ Q r e v T {\displaystyle \mathrm {d} S={\frac {\delta Q_{\mathsf {rev}}}{T}}} Therefore, thermodynamic entropy has
6969-421: The link between the microscopic interactions, which fluctuate about an average configuration, to the macroscopically observable behavior, in form of a simple logarithmic law, with a proportionality constant , the Boltzmann constant , that has become one of the defining universal constants for the modern International System of Units (SI). In his 1803 paper Fundamental Principles of Equilibrium and Movement ,
7070-426: The metabolic pathway (see Allosteric regulation ). The hypothalamic–pituitary–adrenal axis is largely controlled by positive and negative feedback, much of which is still unknown. In psychology , the body receives a stimulus from the environment or internally that causes the release of hormones . Release of hormones then may cause more of those hormones to be released, causing a positive feedback loop. This cycle
7171-421: The microscopic description central to statistical mechanics . The classical approach defines entropy in terms of macroscopically measurable physical properties, such as bulk mass, volume, pressure, and temperature. The statistical definition of entropy defines it in terms of the statistics of the motions of the microscopic constituents of a system — modeled at first classically, e.g. Newtonian particles constituting
7272-455: The mutual interactions of its parts. Feedback is also relevant for the regulation of experimental conditions, noise reduction, and signal control. The thermodynamics of feedback-controlled systems has intrigued physicist since the Maxwell's demon , with recent advances on the consequences for entropy reduction and performance increase. In biological systems such as organisms , ecosystems , or
7373-424: The name of U , but preferring the term entropy as a close parallel of the word energy , as he found the concepts nearly "analogous in their physical significance". This term was formed by replacing the root of ἔργον ('ergon', 'work') by that of τροπή ('tropy', 'transformation'). In more detail, Clausius explained his choice of "entropy" as a name as follows: I prefer going to the ancient languages for
7474-466: The name of that property as entropy . The word was adopted into the English language in 1868. Later, scientists such as Ludwig Boltzmann , Josiah Willard Gibbs , and James Clerk Maxwell gave entropy a statistical basis. In 1877, Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles, in which he defined entropy as proportional to the natural logarithm of
7575-464: The names of important scientific quantities, so that they may mean the same thing in all living tongues. I propose, therefore, to call S the entropy of a body, after the Greek word "transformation". I have designedly coined the word entropy to be similar to energy, for these two quantities are so analogous in their physical significance, that an analogy of denominations seems to me helpful. Leon Cooper added that in this way "he succeeded in coining
7676-474: 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 ( Verwandlungsinhalt in German), of a thermodynamic system or working body of chemical species during a change of state . That was in contrast to earlier views, based on the theories of Isaac Newton , that heat
7777-485: The number of microstates such a gas could occupy. The proportionality constant in this definition, called the Boltzmann constant , has become one of the defining universal constants for the modern International System of Units (SI). Henceforth, the essential problem in statistical thermodynamics has been to determine the distribution of a given amount of energy E over N identical systems. Constantin Carathéodory ,
7878-625: The observed macroscopic state ( macrostate ) of the system. The constant of proportionality is the Boltzmann constant . 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 property — either entropy per unit mass (SI unit: J⋅K ⋅kg ) or entropy per unit amount of substance (SI unit: J⋅K ⋅mol ). Specifically, entropy
7979-470: The other type, many systems with feedback loops cannot be shoehorned into either type, and this is especially true when multiple loops are present. When there are only two parts joined so that each affects the other, the properties of the feedback give important and useful information about the properties of the whole. But when the parts rise to even as few as four, if every one affects the other three, then twenty circuits can be traced through them; and knowing
8080-415: The output of one affecting the input of another, and vice versa. Some systems with feedback can have very complex behaviors such as chaotic behaviors in non-linear systems, while others have much more predictable behaviors, such as those that are used to make and design digital systems. Feedback is used extensively in digital systems. For example, binary counters and similar devices employ feedback where
8181-428: The parameter to maintain is recorded by a reception system and conveyed to a regulation module via an information channel. An example of this is insulin oscillations . Biological systems contain many types of regulatory circuits, both positive and negative. As in other contexts, positive and negative do not imply that the feedback causes good or bad effects. A negative feedback loop is one that tends to slow down
8282-502: The properties of all the twenty circuits does not give complete information about the system. In general, feedback systems can have many signals fed back and the feedback loop frequently contain mixtures of positive and negative feedback where positive and negative feedback can dominate at different frequencies or different points in the state space of a system. The term bipolar feedback has been coined to refer to biological systems where positive and negative feedback systems can interact,
8383-1700: The room) decreases as portions of the thermal energy from the warm surroundings spread to the cooler system of ice and water. Over time the temperature of the glass and its contents and the temperature of the room become equal. In other words, the entropy of the room has decreased as some of its energy has been dispersed to the ice and water, of which the entropy has increased. Feedback Collective intelligence Collective action Self-organized criticality Herd mentality Phase transition Agent-based modelling Synchronization Ant colony optimization Particle swarm optimization Swarm behaviour Social network analysis Small-world networks Centrality Motifs Graph theory Scaling Robustness Systems biology Dynamic networks Evolutionary computation Genetic algorithms Genetic programming Artificial life Machine learning Evolutionary developmental biology Artificial intelligence Evolutionary robotics Reaction–diffusion systems Partial differential equations Dissipative structures Percolation Cellular automata Spatial ecology Self-replication Conversation theory Entropy Feedback Goal-oriented Homeostasis Information theory Operationalization Second-order cybernetics Self-reference System dynamics Systems science Systems thinking Sensemaking Variety Ordinary differential equations Phase space Attractors Population dynamics Chaos Multistability Bifurcation Rational choice theory Bounded rationality Feedback occurs when outputs of
8484-598: The same distinction Black used between "positive feed-back" and "negative feed-back", based not on the sign of the feedback itself but rather on its effect on the amplifier's gain. In contrast, Nyquist and Bode, when they built on Black's work, referred to negative feedback as that with the sign reversed. Black had trouble convincing others of the utility of his invention in part because confusion existed over basic matters of definition. Even before these terms were being used, James Clerk Maxwell had described their concept through several kinds of "component motions" associated with
8585-757: The sign convention for a heat Q {\textstyle Q} transferred in a thermodynamic process ( Q > 0 {\textstyle Q>0} for an absorption and Q < 0 {\textstyle Q<0} for a dissipation) we get: W − Q Σ = W − | Q H | + | Q 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
8686-428: The signal feedback from output is in phase with the input signal, the feedback is called positive feedback. Negative feedback: If the signal feedback is out of phase by 180° with respect to the input signal, the feedback is called negative feedback. As an example of negative feedback, the diagram might represent a cruise control system in a car that matches a target speed such as the speed limit. The controlled system
8787-433: The start of the cycle, hence the change or line integral of any state function, such as entropy, over this reversible cycle is zero. The entropy change d S {\textstyle \mathrm {d} S} of a system excluding its surroundings can be well-defined as a small portion of heat δ Q r e v {\textstyle \delta Q_{\mathsf {rev}}} transferred to
8888-536: The study of any classical thermodynamic heat engine: other cycles, such as an Otto , Diesel or Brayton cycle , could be analyzed from the same standpoint. Notably, any machine or cyclic process converting heat into work (i.e., heat engine) that is claimed to produce an efficiency greater than the one of Carnot is not viable — due to violation of the second law of thermodynamics . For further analysis of sufficiently discrete systems, such as an assembly of particles, statistical thermodynamics must be used. Additionally,
8989-441: The system during reversible process divided by the temperature T {\textstyle T} of the system during this heat transfer : d S = δ Q r e v T {\displaystyle \mathrm {d} S={\frac {\delta Q_{\mathsf {rev}}}{T}}} The reversible process is quasistatic (i.e., it occurs without any dissipation, deviating only infinitesimally from
9090-405: The system's surroundings as a heat. Otherwise, this process cannot go forward. In classical thermodynamics, the entropy of a system is defined if and only if it is in a thermodynamic equilibrium (though a chemical equilibrium is not required: for example, the entropy of a mixture of two moles of hydrogen and one mole of oxygen in standard conditions is well-defined). The statistical definition
9191-413: The system, closing the valve when the required level is reached. This then reoccurs in a circular fashion as the water level fluctuates. Centrifugal governors were used to regulate the distance and pressure between millstones in windmills since the 17th century. In 1788, James Watt designed his first centrifugal governor following a suggestion from his business partner Matthew Boulton , for use in
9292-465: The term entropy from a Greek word for transformation . Austrian physicist Ludwig Boltzmann explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system. He thereby introduced the concept of statistical disorder and probability distributions into a new field of thermodynamics, called statistical mechanics , and found
9393-411: 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 and perfectly stored, represents the decrease in the entropy which could be used to operate the heat engine in reverse, returning to the initial state; thus
9494-460: The total entropy change may still be zero at all times if the entire process is reversible. In contrast, irreversible process increases the total entropy of the system and surroundings. Any process that happens quickly enough to deviate from the thermal equilibrium cannot be reversible, the total entropy increases, and the potential for maximum work to be done during the process is lost. The concept of entropy arose from Rudolf Clausius 's study of
9595-452: The transmission of information in telecommunication . Entropy is central to the second law of thermodynamics , which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward thermodynamic equilibrium , where the entropy is highest. A consequence of the second law of thermodynamics is that certain processes are irreversible . The thermodynamic concept
9696-769: The work W {\textstyle W} as the net heat into the inequality above gives us: Q H T H + Q C T C < 0 {\displaystyle {\frac {Q_{\mathsf {H}}}{T_{\mathsf {H}}}}+{\frac {Q_{\mathsf {C}}}{T_{\mathsf {C}}}}<0} or in terms of the entropy change Δ S r , i {\textstyle \Delta S_{{\mathsf {r}},i}} : Δ S r , H + Δ S r , C > 0 {\displaystyle \Delta S_{\mathsf {r,H}}+\Delta S_{\mathsf {r,C}}>0} A Carnot cycle and an entropy as shown above prove to be useful in
9797-497: Was an indestructible particle that had mass. Clausius discovered that the non-usable energy increases as steam proceeds from inlet to exhaust in a steam engine. From the prefix en- , as in 'energy', and from the Greek word τροπή [tropē], which is translated in an established lexicon as turning or change and that he rendered in German as Verwandlung , a word often translated into English as transformation , in 1865 Clausius coined
9898-440: 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, the thermodynamic definition of entropy provides the experimental verification of entropy, while the statistical definition of entropy extends
9999-515: Was found to vary in the thermodynamic cycle but eventually returned to the same value at the end of every cycle. Thus it was found to be a function of state , specifically a thermodynamic state of the system. 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
10100-512: Was referred to by Scottish scientist and engineer William Rankine in 1850 with the names thermodynamic function and heat-potential . In 1865, German physicist Rudolf Clausius , one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of heat to the instantaneous temperature. He initially described it as transformation-content , in German Verwandlungsinhalt , and later coined
10201-399: Was shown to be useful in characterizing the Carnot cycle . Heat transfer in the isotherm steps (isothermal expansion and isothermal compression) of the Carnot cycle was found to be proportional to the temperature of a system (known as its absolute temperature ). This relationship was expressed in an increment of entropy that is equal to incremental heat transfer divided by temperature. Entropy
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