Non-equilibrium Thermodynamics
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Non-equilibrium Thermodynamics
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. Almost all systems found in nature are not in thermodynamic equilibrium, for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Some systems and processes are, however, in a useful sense, near enough to thermodynamic equilibrium to allow description with useful accuracy by currently known non-equilibrium thermodynamics. Nevertheless, many natural systems and processes will always remain far beyond the scope o ...
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Edward Arthur Milne
Edward Arthur Milne FRS (; 14 February 1896 – 21 September 1950) was a British astrophysicist and mathematician. Biography Milne was born in Hull, Yorkshire, England. He attended Hymers College and from there he won an open scholarship in mathematics and natural science to study at Trinity College, Cambridge in 1914, gaining the largest number of marks which had ever been awarded in the examination. In 1916 he joined a group of mathematicians led by A. V. Hill for the Ministry of munitions working on the ballistics of anti-aircraft gunnery, they became known as ′Hill's Brigands′. Later Milne became an expert on sound localisation. In 1917 he became a lieutenant in the Royal Navy Volunteer Reserve. He was a fellow of Trinity College, Cambridge, 1919–1925, being assistant director of the solar physics observatory, 1920–1924, mathematical lecturer at Trinity, 1924–1925, and university lecturer in astrophysics, 1922–1925. He was Beyer professor of applied mat ...
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Thermoelectric Effect
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa via a thermocouple. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it, heat is transferred from one side to the other, creating a temperature difference. At the atomic scale, an applied temperature gradient causes charge carriers in the material to diffuse from the hot side to the cold side. This effect can be used to generate electricity, measure temperature or change the temperature of objects. Because the direction of heating and cooling is affected by the applied voltage, thermoelectric devices can be used as temperature controllers. The term "thermoelectric effect" encompasses three separately identified effects: the Seebeck effect, Peltier effect, and Thomson effect. The Seebeck and Peltier effects are different manifestations of the same physical process; textbooks may re ...
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Extended Irreversible Thermodynamics
Extended irreversible thermodynamics is a branch of non-equilibrium thermodynamics that goes beyond the local equilibrium hypothesis of classical irreversible thermodynamics. The space of state variables is enlarged by including the fluxes of mass, momentum and energy and eventually higher order fluxes. The formalism is well-suited for describing high-frequency processes and small-length scales materials. Overview Over the last decades, many efforts have been displayed to generalize the classical laws of Fourier (heat conduction), Fick (matter diffusion), Newton (viscous flows) and Ohm (electrical transport). Indeed, modern technology strives towards miniaturized devices, high frequency and strongly non-linear processes requiring for a new conceptual approach. Several classes of theories have been developed with this objective and one of them, known under the heading of ''Extended Irreversible Thermodynamics'' (EIT) has raised a particular growing interest. The paternity of EIT can ...
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Dmitry Zubarev
Dmitry Nikolayevich Zubarev (russian: Дми́трий Никола́евич Зу́барев; November 27, 1917 – July 29, 1992) was a Soviet and Russian theoretical physicist known for his contributions to statistical mechanics, non-equilibrium thermodynamics, plasma physics, theory of turbulence, and to the development of the double-time Green function's formalism. Biography Dmitry Zubarev was born in Moscow in the family of an engineer. In 1941, he graduated from the Physics Department at Moscow State University and soon after that, on 25 June 1941, volunteered to the People's Volunteer Corps to participate in the Second World War. He participated in the Battle of Moscow and met the end of the war in Berlin with the 47th Army of the 1st Belorussian Front. After the war he worked for several years on various military related research projects in Arzamas-16. In this period of time he was greatly influenced by Nikolay Bogolyubov and Andrei Sakharov. Then, in 1954 he moved t ...
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Boltzmann's Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven " defining constants" that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly . Roles of the Boltzmann constant Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure and volume is proportional to the product of amount of ...
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Massieu Function
In thermodynamics, Massieu function (sometimes called Massieu–Gibbs function, Massieu potential, or Gibbs function, or characteristic (state) function in its original terminology), symbol \Psi (Psi), is defined by the following relation: : \Psi = \Psi \big( X_1, \dots, X_i, Y_, \dots Y_r \big) \, where for every system with degree of freedom ''r'' one may choose r variables, e.g. \big( X_1, \dots, X_i, Y_, \dots Y_r \big) \, , to define a coordinate system, where ''X'' and ''Y'' are extensive and intensive variables, respectively, and where at least one extensive variable must be within this set in order to define the size of the system. The (''r'' + 1)-th variable, \Psi , is then called the Massieu function.Inden, Gerhard. (2008). Introduction to Thermodynamics, ''Materials Issues for Generation IV Systems'', pgs. 73–112. Springer The Massieu function was introduced in the 1869 paper "On the Characteristic Functions of Various Fluids" by French eng ...
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Gibbs Free Energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy change , measured in joules in SI) is the ''maximum'' amount of non-expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but not matter) at fixed temperature and pressure. This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state under these conditions, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces. The Gibbs energy is the thermodynamic potential that is minim ...
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Legendre Transformation
In mathematics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involutive transformation on real-valued convex functions of one real variable. In physical problems, it is used to convert functions of one quantity (such as velocity, pressure, or temperature) into functions of the conjugate quantity (momentum, volume, and entropy, respectively). In this way, it is commonly used in classical mechanics to derive the Hamiltonian formalism out of the Lagrangian formalism (or vice versa) and in thermodynamics to derive the thermodynamic potentials, as well as in the solution of differential equations of several variables. For sufficiently smooth functions on the real line, the Legendre transform f^* of a function f can be specified, up to an additive constant, by the condition that the functions' first derivatives are inverse functions of each other. This can be expressed in Euler's derivative notation as Df(\cdot) = \left( D f^* \right) ...
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Helmholtz Free Energy
In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and ...). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium. In contrast, the Gibbs free energy or free enthalpy is most commonly used as a measure of thermodynamic potential (especially in chemistry) when it is convenient for applications that occur at constant ''pressure''. For example, in explosives research Helmholtz ...
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Extensive Quantity
Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is one whose magnitude is independent of the size of the system, whereas an extensive quantity is one whose magnitude is additive for subsystems. The terms ''intensive and extensive quantities'' were introduced into physics by German writer Georg Helm in 1898, and by American physicist and chemist Richard C. Tolman in 1917. An intensive property does not depend on the system size or the amount of material in the system. It is not necessarily homogeneously distributed in space; it can vary from place to place in a body of matter and radiation. Examples of intensive properties include temperature, ''T''; refractive index, ''n''; density, ''ρ''; and hardness, ''η''. By contrast, extensive properties such as the mass, volume and entropy of syste ...
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Complex Fluids
Complex fluids are mixtures that have a coexistence between two phases: solid–liquid (suspensions or solutions of macromolecules such as polymers), solid–gas (granular), liquid–gas (foams) or liquid–liquid (emulsions). They exhibit unusual mechanical responses to applied stress or strain due to the geometrical constraints that the phase coexistence imposes. The mechanical response includes transitions between solid-like and fluid-like behavior as well as fluctuations. Their mechanical properties can be attributed to characteristics such as high disorder, caging, and clustering on multiple length scales. Example Shaving cream is an example of a complex fluid. Without stress, the foam appears to be a solid: it does not flow and can support (very) light loads. However, when adequate stress is applied, shaving cream flows easily like a fluid. On the level of individual bubbles, the flow is due to rearrangements of small collections of bubbles. On this scale, the fl ...
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Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow. A laser differs from other sources of light in that it emits light which is ''coherent''. Spatial coherence allows a laser to be focused to a tight spot, enabling applications such as laser cutting and lithography. Spatial coherence also allows a laser beam to stay narrow over great distances (collimation), enabling applications such as laser pointers and lidar (light detection and ranging). Lasers can also have high temporal coherence, which allows them to emit light with a very narrow spectrum. Alternatively, temporal coherence can be used to produce ultrashort pulses of ligh ...
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