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26 relations: Activation energy, Boltzmann distribution, Canonical ensemble, Density of states, Detailed balance, Dirac delta function, Equation of State Calculations by Fast Computing Machines, Estimator, Hamiltonian (quantum mechanics), Importance sampling, Integral, Ising model, Markov chain Monte Carlo, Maxima and minima, Metropolis–Hastings algorithm, Monte Carlo integration, Phase transition, Physics, Potts model, Random walk, Spin (physics), Spin glass, Statistics, Stochastic drift, Wang and Landau algorithm, Wolff algorithm.
Activation energy
In chemistry and physics, activation energy is the energy which must be available to a chemical or nuclear system with potential reactants to result in: a chemical reaction, nuclear reaction, or other various other physical phenomena.
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Boltzmann distribution
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution, probability measure, or frequency distribution of particles in a system over various possible states.
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Canonical ensemble
In statistical mechanics, a canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature.
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Density of states
In solid-state and condensed matter physics, the density of states (DOS) of a system describes the number of states per interval of energy at each energy level available to be occupied.
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Detailed balance
The principle of detailed balance is formulated for kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions): At equilibrium, each elementary process should be equilibrated by its reverse process.
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Dirac delta function
In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.
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Equation of State Calculations by Fast Computing Machines
Equation of State Calculations by Fast Computing Machines is an article published by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller in the Journal of Chemical Physics in 1953.
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Estimator
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished.
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Hamiltonian (quantum mechanics)
In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.
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Importance sampling
In statistics, importance sampling is a general technique for estimating properties of a particular distribution, while only having samples generated from a different distribution than the distribution of interest.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Ising model
The Ising model, named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics.
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Markov chain Monte Carlo
In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution.
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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Metropolis–Hastings algorithm
In statistics and in statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution for which direct sampling is difficult.
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Monte Carlo integration
In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers.
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Phase transition
The term phase transition (or phase change) is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Potts model
In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice.
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Random walk
A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.
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Spin (physics)
In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.
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Spin glass
A spin glass is a disordered magnet, where the magnetic spins of the component atoms (the orientation of the north and south magnetic poles in three-dimensional space) are not aligned in a regular pattern. The term "glass" comes from an analogy between the magnetic disorder in a spin glass and the positional disorder of a conventional, chemical glass, e.g., a window glass. In window glass or any amorphous solid the atomic bond structure is highly irregular; in contrast, a crystal has a uniform pattern of atomic bonds. In ferromagnetic solid, magnetic spins all align in the same direction; this would be analogous to a crystal. The individual atomic bonds in a spin glass are a mixture of roughly equal numbers of ferromagnetic bonds (where neighbors have the same orientation) and antiferromagnetic bonds (where neighbors have exactly the opposite orientation: north and south poles are flipped 180 degrees). These patterns of aligned and misaligned atomic magnets create what are known as frustrated interactions - distortions in the geometry of atomic bonds compared to what would be seen in a regular, fully aligned solid. They may also create situations where more than one geometric arrangement of atoms is stable. Spin glasses and the complex internal structures that arise within them are termed "metastable" because they are "stuck" in stable configurations other than the lowest-energy configuration (which would be aligned and ferromagnetic). The mathematical complexity of these structures is difficult but fruitful to study experimentally or in simulations, with applications to artificial neural networks in computer science, in addition to physics, chemistry, and materials science.
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Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
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Stochastic drift
In probability theory, stochastic drift is the change of the average value of a stochastic (random) process.
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Wang and Landau algorithm
The Wang and Landau algorithm, proposed by Fugao Wang and David P. Landau, is a Monte Carlo method designed to estimate the density of states of a system.
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Wolff algorithm
The Wolff algorithm, named after Ulli Wolff, is an algorithm for Monte Carlo simulation of the Ising model in which the unit to be flipped is not a single spin, as in the heat bath or Metropolis algorithms, but a cluster of them.
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References
[1] https://en.wikipedia.org/wiki/Multicanonical_ensemble
