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Green–Kubo Relations
The Green–Kubo relations ( Melville S. Green 1954, Ryogo Kubo 1957) give the exact mathematical expression for a transport coefficient \gamma in terms of the integral of the equilibrium time correlation function of the time derivative of a corresponding microscopic variable A (sometimes termed a "gross variable", as in ): \gamma = \int_0^\infty \left\langle \dot(t) \dot(0) \right\rangle \;t. One intuitive way to understand this relation is that relaxations resulting from random fluctuations in equilibrium are indistinguishable from those due to an external perturbation in linear response. Green-Kubo relations are important because they relate a macroscopic transport coefficient to the correlation function of a microscopic variable. In addition, they allow one to measure the transport coefficient without perturbing the system out of equilibrium, which has found much use in molecular dynamics simulations. Thermal and mechanical transport processes Thermodynamic systems m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melville S
Melville may refer to: Places Antarctica *Cape Melville (South Shetland Islands) *Melville Peak, King George Island * Melville Glacier, Graham Land * Melville Highlands, Laurie Island * Melville Point, Marie Byrd Land Australia *Cape Melville, Queensland *City of Melville, Western Australia, the local government authority *Electoral district of Melville, Western Australia * Melville Bay, Northern Territory *Melville Island, Northern Territory *Melville, Western Australia, a suburb of Perth Canada *Melville, Saskatchewan, a city *Melville (electoral district), Saskatchewan, a federal electoral district *Melville (provincial electoral district), Saskatchewan *Lake Melville, Newfoundland and Labrador *Melville Peninsula, Nunavut *Melville Sound, Nunavut *Melville Island (Northwest Territories and Nunavut) *Melville Island (Nova Scotia), in Halifax Harbour *Melville Cove, Halifax, in Halifax Harbour * Melville, Inverness County, Nova Scotia * Melville, Pictou County, Nova Scotia * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluctuation Theorem
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the Entropy (statistical thermodynamics), entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time. While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously ''decrease''; the fluctuation theorem precisely quantifies this probability. Statement Roughly, the fluctuation theorem relates to the probability distribution of the time-averaged irreversible entropy production, denoted \overline_t. The theorem states that, in systems away from equilibrium over a fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Equations
Thermodynamics is expressed by a mathematical framework of ''thermodynamic equations'' which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics. Introduction One of the fundamental thermodynamic equations is the description of thermodynamic work in analogy to mechanical work, or weight lifted through an elevation against gravity, as defined in 1824 by French physicist Sadi Carnot. Carnot used the phrase motive power for work. In the footnotes to his famous ''On the Motive Power of Fire'', he states: “We use here the expression ''motive power'' to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.” With the in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Response Function
A linear response function describes the input-output relationship of a signal transducer, such as a radio turning electromagnetic waves into music or a neuron turning synaptic input into a response. Because of its many applications in information theory, physics and engineering there exist alternative names for specific linear response functions such as susceptibility, impulse response or impedance; see also transfer function. The concept of a Green's function or fundamental solution of an ordinary differential equation is closely related. Mathematical definition Denote the input of a system by h(t) (e.g. a force), and the response of the system by x(t) (e.g. a position). Generally, the value of x(t) will depend not only on the present value of h(t), but also on past values. Approximately x(t) is a weighted sum of the previous values of h(t'), with the weights given by the linear response function \chi(t-t'): x(t) = \int_^t dt'\, \chi(t-t') h(t') + \cdots\,. The explicit te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lindblad Equation
In quantum mechanics, the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation (named after Vittorio Gorini, Andrzej Kossakowski, E. C. George Sudarshan, George Sudarshan and Göran Lindblad (physicist), Göran Lindblad), master equation in Lindblad form, quantum Liouvillian, or Lindbladian is one of the general forms of Markov process, Markovian Quantum master equation, master equations describing open quantum systems. It generalizes the Schrödinger equation to open quantum systems; that is, systems in contacts with their surroundings. The resulting dynamics are no longer unitary, but still satisfy the property of being completely positive trace-preserving, trace-preserving and completely positive for any initial condition. The Schrödinger equation or, actually, the von Neumann equation, is a special case of the GKSL equation, which has led to some speculation that quantum mechanics may be productively extended and expanded through further application and analysis of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Green's Function (many-body Theory)
In many-body theory, the term Green's function (or Green function) is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators. The name comes from the Green's functions used to solve inhomogeneous differential equations, to which they are loosely related. (Specifically, only two-point "Green's functions" in the case of a non-interacting system are Green's functions in the mathematical sense; the linear operator that they invert is the Hamiltonian operator, which in the non-interacting case is quadratic in the fields.) Spatially uniform case Basic definitions We consider a many-body theory with field operator (annihilation operator written in the position basis) \psi(\mathbf). The Heisenberg operators can be written in terms of Schrödinger operators as \psi(\mathbf,t) = e^ \psi(\mathbf) e^, and the creation operator is \bar\psi(\mathbf,t) = psi(\mathbf,t)\dagger, where K = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluctuation–dissipation Theorem
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance. Given that a system obeys detailed balance, the theorem is a proof that thermodynamic fluctuations in a physical variable predict the response quantified by the admittance or impedance (in their general sense, not only in electromagnetic terms) of the same physical variable (like voltage, temperature difference, etc.), and vice versa. The fluctuation–dissipation theorem applies both to classical and quantum mechanical systems. The fluctuation–dissipation theorem was proven by Herbert Callen and Theodore Welton in 1951 and expanded by Ryogo Kubo. There are antecedents to the general theorem, including Einstein's explanation of Brownian motion during his '' annus mirabilis'' and Harry Nyquist's explanation in 1928 of Johnson noise in electrical resistors. Qualitative overview a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluctuation Theorem
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the Entropy (statistical thermodynamics), entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time. While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously ''decrease''; the fluctuation theorem precisely quantifies this probability. Statement Roughly, the fluctuation theorem relates to the probability distribution of the time-averaged irreversible entropy production, denoted \overline_t. The theorem states that, in systems away from equilibrium over a fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Matrix
In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed states. These arise in quantum mechanics in two different situations: # when the preparation of a system can randomly produce different pure states, and thus one must deal with the statistics of possible preparations, and # when one wants to describe a physical system that is entangled with another, without describing their combined state. This case is typical for a system interacting with some environment (e.g. decoherence). In this case, the density matrix of an entangled system differs from that of an ensemble of pure states that, combined, would give the same statistical results upon measurement. Density matrices are thus crucial tools in areas of quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Law Of Thermodynamics
The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient). Another statement is: "Not all heat can be converted into Work (thermodynamics), work in a cyclic process."Young, H. D; Freedman, R. A. (2004). ''University Physics'', 11th edition. Pearson. p. 764. The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. It predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Zwanzig
Robert Walter Zwanzig (9 April 1928 – May 15, 2014) was an American theoretical physicist and chemist who made important contributions to the statistical mechanics of irreversible processes, protein folding, and the theory of liquids and gases. Background Zwanzig received his bachelor's degree from Brooklyn Polytechnic Institute in 1948 and his master's degree from 1950 at the University of Southern California. In 1952 he completed a doctorate in physical chemistry at Caltech under the supervision of John G. Kirkwood. His thesis title was ''Quantum Hydrodynamics: a statistical mechanical theory of light scattering from simple non-polar fluids''. From 1951 to 1954 he worked as a post-doctoral researcher in theoretical chemistry at Yale University, and from 1954 to 1958 he was an assistant professor in chemistry at Johns Hopkins University. From 1958 to 1966 he was a physical chemist at the National Bureau of Standards and from 1966 to 1979 he was a research professor at the In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
