Entropy Entropy is a scientific concept, as well as a measurable physical property, 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 thermodyna ...

, in thermodynamics, is a property originally introduced to explain the part of the internal energy of a thermodynamic system that is unavailable as a source for useful work. Entropy may also refer to:

Thermodynamics and statistical mechanics

Entropy (classical thermodynamics) In classical thermodynamics, entropy is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid-nineteenth century from the Greek word ...

, thermodynamic entropy in macroscopic terms, with less emphasis on the statistical explanation **

Entropic force In physics, an entropic force acting in a system is an emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale. Mathematical form ...

. The product of temperature and the gradient of the entropy density is viewed an effective force, yielding a gradient in the energy density of a system. **

Entropy production Entropy production (or generation) is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anelastic ...

. Development of entropy in a thermodynamic system. *

Entropy (statistical thermodynamics) The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy ...

, the statistical explanation of thermodynamic entropy based on probability theory **

Configuration entropy In statistical mechanics, configuration entropy is the portion of a system's entropy that is related to discrete representative positions of its constituent particles. For example, it may refer to the number of ways that atoms or molecules pack tog ...

, the entropy change due to a change in the knowledge of the position of particles, rather than their momentum **

Conformational entropy In chemical thermodynamics, conformational entropy is the entropy associated with the number of conformations of a molecule. The concept is most commonly applied to biological macromolecules such as proteins and RNA, but also be used for polysa ...

, the entropy change due to a change in the "configuration" of a particle (e.g. a right-handed vs. a left-handed polyatomic molecule) * Kaniadakis κ-entropy, which is a generalization of Boltzmann-Gibbs entropy. *

Tsallis entropy In physics, the Tsallis entropy is a generalization of the standard Boltzmann–Gibbs entropy. Overview The concept was introduced in 1988 by Constantino Tsallis as a basis for generalizing the standard statistical mechanics and is identical in fo ...

, a generalization of Boltzmann-Gibbs entropy *

von Neumann entropy In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics. For a quantum-mechanical system described by a density matrix ...

, entropy in quantum statistical physics and quantum information science

Introductory articles

Introduction to entropy In thermodynamics, entropy is a numerical quantity that shows that many physical processes can go in only one direction in time. For example, you can pour cream into coffee and mix it, but you cannot "unmix" it; you can burn a piece of wood, but ...

an explanation on entropy as a measure of irreversibility *

Entropy (order and disorder) In thermodynamics, entropy is often associated with the amount of order or disorder in a thermodynamic system. This stems from Rudolf Clausius' 1862 assertion that any thermodynamic process always "admits to being reduced eductionto the alteratio ...

, the relationship of disorder with heat and work * Entropy in thermodynamics and information theory, the relationship between thermodynamic entropy and information (Shannon) entropy * Entropy (energy dispersal), dispersal of energy as a descriptor of entropy

Other aspects

History of entropy The concept of entropy developed in response to the observation that a certain amount of functional energy released from combustion reactions is always lost to dissipation or friction and is thus not transformed into useful work. Early heat-powere ...

Entropy and life Research concerning the relationship between the thermodynamic quantity entropy and the evolution of life began around the turn of the 20th century. In 1910, American historian Henry Adams printed and distributed to university libraries and histor ...

, the relationship between the thermodynamic entropy and the evolution of life * Entropy (astrophysics), the adiabatic constant

Information theory and mathematics

Entropy (information theory) In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable X, which takes values in the alphabet \ ...

, also called Shannon entropy, a measure of the unpredictability or information content of a message source *

Differential entropy Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy, a measure of average surprisal of a random variable, to continuo ...

, a generalization of

to continuous random variables **

Entropy of entanglement The entropy of entanglement (or entanglement entropy) is a measure of the degree of quantum entanglement between two subsystems constituting a two-part composite quantum system. Given a pure bipartite quantum state of the composite system, it is p ...

, related to the Shannon and von Neumann entropies for entangled systems; reflecting the degree of entanglement of subsystems * Algorithmic entropy an (incomputable) measure of the information content of a particular message *

Rényi entropy In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. The Rényi entropy is named after Alfréd Rényi, who looked for t ...

, a family of diversity measures generalising Shannon entropy; used to define fractal dimensions * Measure theoretic entropy, a measure of exponential growth in dynamical systems; equivalent to the rate of increase of Shannon entropy of a trajectory in trajectory-space *

Topological entropy In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

, a measure of exponential growth in dynamical systems; equivalent to the rate of increase of α->0 Renyi entropy of a trajectory in trajectory-space. * Topological entropy in physics * Volume entropy, a Riemannian invariant measuring the exponential rate of volume growth of a Riemannian metric * Maximum entropy (disambiguation) * Graph entropy, a measure of the information rate achievable by communicating symbols over a channel in which certain pairs of values may be confused.

Other uses in science and technology

Entropy encoding In information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method ...

, data compression strategies to produce a code length equal to the entropy of a message *

Entropy (computing) In computing, entropy is the randomness collected by an operating system or application for use in cryptography or other uses that require random data. This randomness is often collected from hardware sources (variance in fan noise or HDD), eithe ...

, an indicator of the number of random bits available to seed cryptography systems * Entropy (anesthesiology), a measure of a patient's cortical function, based on the mathematical entropy of EEG signals * Entropy (ecology), measures of biodiversity in the study of biological ecology, based on Shannon and Rényi entropies *

Social entropy Social entropy is a sociological theory that evaluates social behaviours using a method based on the second law of thermodynamics. The equivalent of entropy in a social system is considered to be wealth or residence location. The theory was introd ...

, a measure of the natural decay within a social system

Media

* Entropy (choreography) - the difference between a transcription and a performance

Film and television

* ''Entropy'' (film), a 1999 film by Phil Joanou * "Entropy" (''Buffy'' episode) * "Entropy", an episode of ''Criminal Minds'' (season 11)

Games

* ''Entropy'' (1977 board game) * ''Entropy'' (video game) * Entropy or Alchemiss, a character in '' Freedom Force vs the 3rd Reich'' * N. Tropy, a character from Crash Bandicoot: Warped

Literature

*'' Entropy: A New World View'', a book by Jeremy Rifkin and Ted Howard *"Entropy", a 1960 short story by

Thomas Pynchon Thomas Ruggles Pynchon Jr. ( , ; born May 8, 1937) is an American novelist noted for his dense and complex novels. His fiction and non-fiction writings encompass a vast array of subject matter, genres and themes, including history, music, scie ...

*"Entropy", a 1995 short story by

Leanne Frahm Leanne Frahm is an Australian writer of speculative short fiction. Biography Frahm was born in Brisbane, Queensland, Australia in 1946. She received her first nomination for her work in 1978 when she was a finalist for the 1979 Ditmar Award ...

* ''Entropy'' (journal), a scientific journal published by MDPI * ''Entropy'' (magazine), an online literary magazine

Music

* ''Entropy'' (album), an album by Anathallo and Javelins * '' Entropy / Send Them'', an EP by DJ Shadow and the Groove Robbers * "Entropy", a song by Bad Religion from '' Against the Grain'' * "Entropy", a song by Kelly Osbourne from ''

Sleeping in the Nothing ''Sleeping in the Nothing'' is the second and most recent studio album by Kelly Osbourne, released in 2005. Unlike the pop punk sound of her first album, ''Sleeping in the Nothing'' features Osbourne singing to '80s-inspired electro beats. For t ...

'' * "Entropy", a song by VNV Nation from '' Matter + Form'' * "Entropy", a song by Moxy Früvous from '' The 'b' Album'' * "Entropy", a song by Brymo from ''

Oṣó ''Oṣó'' (Yoruba: ''The Wizard'') is the sixth studio album by Nigerian singer Brymo. It was released independently on 27 March 2018. The album was produced entirely by Mikky Me Joses and consists of 11 tracks, including three recorded in the ...

'' * "Entropy", a song by Daniel Caesar from ''

Case Study 01 ''Case Study 01'' (stylized in all caps) is the second studio album by Canadian singer and songwriter Daniel Caesar, released on June 28, 2019, through Golden Child Recordings. It features guest appearances from Brandy, Pharrell Williams, John Ma ...

'' * "Entropy", a song by

MC Hawking Ken Lawrence is a nerdcore rapper who purports to be the late theoretical physicist Stephen Hawking rapping under the name MC Hawking. MC Hawking rose to popularity on the Internet in the early 2000s. The songs were originally released in MP3 fo ...

* "Entropy", a song by Grimes and

Bleachers Bleachers (North American English), or stands, are raised, tiered rows of benches found at sports fields and other spectator events. Stairways provide access to the horizontal rows of seats, often with every other step gaining access to a row ...

* ''Entropia'' (album), an album by Pain of Salvation *Entropy, a track by

Nigel Stanford Nigel Stanford (full name: Nigel John Stanford) is a New Zealand composer, best known for his soundtrack for the movie '' TimeScapes'' directed by Tom Lowe, as well as his music videos ''Cymatics'' and ''Automatica''. In January 2019, a Huawei ...

*''The Book Of Us: Entropy'', an album by

DAY6 Day6 (; stylized in all caps) is a South Korean pop rock band under the label JYP Entertainment. The group debuted on September 7, 2015, with the EP ''The Day,'' which peaked at No.2 on ''Billboard''s World Album Chart a week following its r ...

Software

* Entropy (package manager), a Sabayon Linux package manager {{disambig