In the physics, entropy is a differential term "dQ/T", where dQ is the amount of heat absorbed reversibly by a thermodynamic system at a temperature T, introduced in the early 1860s by the German physicist Rudolf Clausius to mathematically account for the dissipation of energy in thermodynamic systems in which work is produced. Clausius coined the term based on the Greek entrepein meaning "energy turned inward". Although the concept of entropy is primarily a thermodynamic construct, it has since expanded into many different fields of study, such as: statistical mechanics, thermal physics, information theory, psychodynamics, economics, and evolution, to name a few.
"Ice melting" - a classic example of entropy increasingContents [hide]
1 Overview
2 History
3 Thermodynamic definition
3.1 Units and symbols
4 Statistical interpretation
5 Information theory
6 The second law
7 The arrow of time
8 Entropy and cosmology
9 Entropy in fiction
10 See also
11 References
12 External links
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Overview
Many quantities of matter tend to equalize their thermodynamic parameters - reducing differentials towards zero. Pressure differences, density differences, and temperature differences, all tend towards equalizing. Entropy is a measure of how far along this process of equalization has come. Entropy increases as this equalization process advances. For example, the combined entropy of "a cup of hot water in a cool room" is less than the entropy of "the room and the water after it has cooled (and warmed the room slightly)," because the heat is more evenly distributed. The entropy of the room and the empty cup after the water has evaporated is even higher.
In thermodynamics, entropy is often described as "a measure of the disorder, or mixedupness, of a thermodynamic system". This has led many people to misinterpret the meaning of entropy because, unless the disorder is on the molecular scale, any entropy associated with disorder is very small. However, "mixedupness" and "disorder" can be formally defined in a way that is consistent with the realities of entropy: a system that is more "disordered" or more "mixed up" (on a molecular scale) is equivalently also "a system with a lower amount of energy available to do work" or "a system in a macroscopically more probable state".
In fact, the entropy of a thermodynamic system can be interpreted in two distinct, but compatible, ways:
From a macroscopic perspective, in classical thermodynamics the entropy is interpreted simply 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. The state function has the important property that, when multiplied by a reference temperature, it can be understood as a measure of the amount of energy in a physical system that cannot be used to do thermodynamic work; i.e., work mediated by thermal energy. More precisely, in any process where the system gives up energy ΔE, and its entropy falls by ΔS, a quantity at least TR ΔS of that energy must be given up to the system's surroundings as unusable heat (TR is the temperature of the system's external surroundings). Otherwise the process will not go forward.
From a microscopic perspective, in statistical thermodynamics the entropy is envisioned as a measure of the number of microscopic configurations that are capable of yielding the observed macroscopic description of the thermodynamic system. A more "disordered" or "mixed up" system can thus be formally defined, as one which has more microscopic states compatible with the macroscopic description. It can be shown that this definition of entropy, sometimes referred to as Boltzmann's postulate, reproduces all of the properties of the entropy of classical thermodynamics.
An important law of physics, the second law of thermodynamics, states that the total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value. Unlike almost all other laws of physics, this associates thermodynamics with a definite arrow of time.
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History
Main article: History of entropy
The short history of entropy begins with the work of mathematician Lazare Carnot who in his 1803 work Fundamental Principles of Equilibrium and Movement postulated that in any machine the accelerations and shocks of the moving parts all represent losses of moment of activity. In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy. Building on this work, in 1824 Lazare’s son Sadi Carnot published Reflections on the Motive Power of Fire in which he set forth the view that in all heat engines “caloric”, or what is now known as heat, moves from hot to cold and that “some caloric is always lost”. This lost caloric was a precursory form of entropy loss as we now know it. Though formulated in terms of caloric, rather than entropy, this was an early insight into the second law of thermodynamics. In the 1850s, Rudolf Clausius gave this “lost caloric” a mathematical interpretation and called it entropy. Later, scientists such as Ludwig Boltzmann, Willard Gibbs, and James Clerk Maxwell gave entropy a statistical basis. Carathéodory linked entropy with a mathematical definition of irreversiblity, in terms of trajectories and integrability.
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Thermodynamic definition
Main article: Entropy (thermodynamic views)
In the early 1850s, Rudolf Clausius put the concept of “energy turned to waste” on a differential footing. Essentially, he set forth the concept of the thermodynamic system and positioned the argument that in any irreversible process a small amount of heat energy dQ is incrementally dissipated across the system boundary. In 1876, chemical engineer Willard Gibbs, building on the work of those as Clausius and Hermann von Helmholtz, situated the view that the measurement of “available energy” ΔG in a thermodynamic system could be mathematically accounted for by subtracting the “energy loss” TΔS from total energy change of the system ΔH. These concepts were further developed by those as James Clerk Maxwell [1871] and Max Planck [1903].
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Units and symbols
Conjugate variables
of thermodynamics
Pressure Volume
Temperature Entropy
Chem. potential Particle no.
Entropy is the measure of disorder. It is a key physical variable in describing a thermodynamic system. The SI unit of entropy is 'joule per kelvin' (J·K−1), which is the same as the unit of heat capacity, and entropy is said to be thermodynamically conjugate to temperature. The entropy depends only on the current state of the system, not its detailed previous history, and so it is a state function of the parameters like pressure, temperature, etc., which describe the observable macroscopic properties of the system. Entropy is usually symbolized by the letter S.
There is an important connection between entropy and the amount of internal energy in the system which is not available to perform work. In any process where the system gives up an energy ΔE, and its entropy falls by ΔS, a quantity at least TR ΔS of that energy must be given up to the system's surroundings as unusable heat. Otherwise the process will not go forward. (TR is the temperature of the system's external surroundings, which may not be the same as the system's current temperature T ).
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Statistical interpretation
Main article: Entropy (statistical views)
In 1877, thermodynamicist Ludwig Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles, in which he defined entropy to be proportional to the logarithm of the number of microstates such a gas could occupy. Henceforth, the essential problem in statistical thermodynamics, i.e. according to Erwin Schrodinger, has been to determine the distribution of a given amount of energy E over N identical systems.
Statistical mechanics explains entropy as the amount of uncertainty (or "mixedupness" in the phrase of Gibbs) which remains about a system, after its observable macroscopic properties have been taken into account. For a given set of macroscopic quantities, like temperature and volume, the entropy measures the degree to which the probability of the system is spread out over different possible quantum states. The more states available to the system with higher probability, the greater the "disorder" and thus, the greater the entropy.
On the molecular scale, the two definitions match up because adding heat to a system, which increases its classical thermodynamic entropy, also increases the system's thermal fluctuations, so giving an increased lack of information about the exact microscopic state of the system, i.e. an increased statistical mechanical entropy.
It should be noted that the "disorder", in this sense, is dominated by the different arrangements possible on a molecular scale. There is entropy associated with macroscopic disorder (eg a shuffled pack of cards, or the messy distribution of objects in a room); but it is quite negligible, because the number of macroscopic objects is tiny compared to the number of molecules. The entropy produced by the heat in your muscles while shuffling an ordered pack of cards is not negligible, because it is molecular in scale, while the entropy involved in disordering the cards is completely negligibile.
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Information theory
Main article: Information entropy,
Main article: Entropy in thermodynamics and information theory
The concept of entropy in information theory describes with how much randomness (or, alternatively, 'uncertainty') there is in a signal or random event. An alternative way to look at this is to talk about how much information is carried by the signal.
The entropy in statistical mechanics can be considered to be a specific application of Shannon entropy, according to a viewpoint known as MaxEnt thermodynamics. Roughly speaking, Shannon entropy is proportional to the minimum number of yes/no questions you have to ask to get the answer to some question. The statistical mechanical entropy is then proportional to the minimum number of yes/no questions you have to ask in order to determine the microstate, given that you know the macrostate.
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The second law
Main article: Second law of thermodynamics
An important law of physics, the second law of thermodynamics, states that the total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value; and so, by implication, the entropy of the universe as a whole (i.e. the system and its surroundings) tends to increase. We will consider the meaning of the "second law" further in a subsequent section. Two important consequences are that heat cannot of itself pass from a colder to a hotter body: i.e., it is impossible to transfer heat from a cold to a hot reservoir without at the same time converting a certain amount of work to heat. It is also impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work; it can only get useful work out of the heat if heat is at the same time transferred from a hot to a cold reservoir. This means that there is no possibility of a 'perpetuum mobile' which is isolated. Also, from this it follows, that a reduction in the increase of entropy in a specified process, such as a chemical reaction, means that it is energetically more efficient.
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The arrow of time
Main article: Entropy (arrow of time)
Entropy is the only quantity in the physical sciences that "picks" a particular direction for time, sometimes called an arrow of time. As we go "forward" in time, the Second Law of Thermodynamics tells us that the entropy of an isolated system can only increase or remain the same; it cannot decrease. Hence, from one perspective, entropy measurement is thought of as a kind of clock.
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Entropy and cosmology
We have previously mentioned that the universe may be considered an isolated system. As such, it may be subject to the Second Law of Thermodynamics, so that its total entropy is constantly increasing. It has been speculated that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source.
If the universe can be considered to have increasing entropy, then, as Roger Penrose has pointed out, an important role in the disordering process is played by gravity, which causes dispersed matter to accumulate into stars, which collapse eventually into black holes. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size. This makes them likely end points of all entropy-increasing processes.
The role of entropy in cosmology remains a controversial subject. Recent work has cast extensive doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in an expanding universe, the maximum possible entropy rises much more rapidly and leads to an "entropy gap," thus pushing the system further away from equilibrium with each time increment. Complicating factors, such as the energy density of the vacuum and macroscopic quantum effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult.
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Entropy in fiction
Martin Amis's Time's Arrow, a novel written in reverse.
Isaac Asimov's "The Last Question," a short science fiction story about entropy
Thomas Pynchon, an American author who deals with entropy in many of his novels
Diane Duane's Young Wizards series, in which the protagonists' ultimate goal is to slow down entropy and delay heat death.
Gravity Dreams by L.E. Modesitt Jr.
The Planescape setting for Dungeons & Dragons includes the Doomguard faction, who worship entropy.
Arcadia, a play by Tom Stoppard, explores entropy, the arrow of time, and heat death.
Stargate SG-1 and Atlantis, science-fiction television shows where a ZPM (Zero Point Module) is depleted when it reaches maximum entropy
In DC Comics's series Zero Hour, entropy plays a central role in the continuity of the universe.
"Time's Arrow," a two-part episode of Star Trek: The Next Generation
H.G. Wells' story "The Time Machine" had a theme that was based upon entropy and how instead of humans evolving, they in fact devolved into two species
"Logopolis," an episode of Doctor Who
Asemic Magazine Asemic Magazine is an Australian publication that is exploring entropy in literature.
Philip K. Dick's "UBIK" a science fiction novel with entropy as underlying theme.