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Detailed Balance
The principle of detailed balance can be used in Kinetics (physics), kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions). It states that at Thermodynamic equilibrium, equilibrium, each elementary process is in equilibrium with its reverse process. History The principle of detailed balance was explicitly introduced for collisions by Ludwig Boltzmann. In 1872, he proved his H-theorem using this principle.Boltzmann, L. (1964), Lectures on gas theory, Berkeley, CA, USA: U. of California Press. The arguments in favor of this property are founded upon microscopic reversibility.Richard C. Tolman, Tolman, R. C. (1938). ''The Principles of Statistical Mechanics''. Oxford University Press, London, UK. Five years before Boltzmann, James Clerk Maxwell used the principle of detailed balance for gas kinetics with the reference to the principle of sufficient reason. He compared the idea of detailed balance with other types of balancing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetics (physics)
In physics and engineering, kinetics is the branch of classical mechanics that is concerned with the relationship between the motion In physics, motion is when an object changes its position with respect to a reference point in a given time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of reference to an o ... and its causes, specifically, forces and torques. Since the mid-20th century, the term "Dynamics (mechanics), dynamics" (or "analytical dynamics") has largely superseded "kinetics" in physics textbooks, though the term is still used in engineering. In Plasma (physics), plasma physics, kinetics refers to the study of Continuum mechanics, continua in velocity space. This is usually in the context of non-thermal (Maxwell–Boltzmann distribution#Physical applications, non-Maxwellian) velocity distributions, or processes that Perturbation theory (quantum mechanics), perturb thermal distributions. These ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Chemistry
Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mechanics, analytical dynamics and chemical equilibria. Physical chemistry, in contrast to chemical physics, is predominantly (but not always) a supra-molecular science, as the majority of the principles on which it was founded relate to the bulk rather than the molecular or atomic structure alone (for example, chemical equilibrium and colloids). Some of the relationships that physical chemistry strives to understand include the effects of: # Intermolecular forces that act upon the physical properties of materials ( plasticity, tensile strength, surface tension in liquids). # Reaction kinetics on the rate of a reaction. # The identity of ions and the electrical conductivity of materials. # Surface science and electrochemistry of cell m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugh Everett
Hugh Everett III (; November 11, 1930 – July 19, 1982) was an American physicist who proposed the relative state interpretation of quantum mechanics. This influential approach later became the basis of the many-worlds interpretation (MWI). Everett's theory dropped the wave function collapse postulate of quantum measurement theory, incorporating the observer in the same quantum state as the observation result. The quantum statistic becomes a measure of the branching of the universal wave function. Everett also helped found small companies specializing in contracts with the US government. Although largely disregarded until near the end of his life, Everett's work received more credibility with the discovery of quantum decoherence in the 1970s and has received increased attention in recent decades, with MWI becoming one of the important interpretations of quantum mechanics. Early life and education Hugh Everett III was born in 1930 and raised in the Washington, D.C. area. Hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of the Information Age. Shannon was the first to describe the use of Boolean algebra—essential to all digital electronic circuits—and helped found artificial intelligence (AI). Roboticist Rodney Brooks declared Shannon the 20th century engineer who contributed the most to 21st century technologies, and mathematician Solomon W. Golomb described his intellectual achievement as "one of the greatest of the twentieth century". At the University of Michigan, Shannon dual degreed, graduating with a Bachelor of Science in electrical engineering and another in mathematics, both in 1936. A 21-year-old master's degree student in electrical engineering at MIT, his thesis, "A Symbolic Analysis of Relay and Switching Circuits", demonstrated that electric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hendrik Lorentz
Hendrik Antoon Lorentz ( ; ; 18 July 1853 – 4 February 1928) was a Dutch theoretical physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for their discovery and theoretical explanation of the Zeeman effect. He derived the Lorentz transformation of the special theory of relativity, as well as the Lorentz force, which describes the combined electric and magnetic forces acting on a charged particle in an electromagnetic field. Lorentz was also responsible for the Lorentz oscillator model, a classical model used to describe the anomalous dispersion observed in dielectric materials when the driving frequency of the electric field was near the resonant frequency of the material, resulting in abnormal refractive indices. According to the biography published by the Nobel Foundation, "It may well be said that Lorentz was regarded by all theoretical physicists as the world's leading spirit, who completed what was left unfinished by his predecessors and prepar ... [...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] |
Aizik Isaakovich Vol'pert
Aizik Isaakovich Vol'pert (; 5 June 1923 – January 2006) (the family name is also transliterated as Volpert or WolpertSee .) was a Soviet and Israeli mathematician and chemical engineer working in partial differential equations, functions of bounded variation and chemical kinetics. Life and academic career Vol'pert graduated from Lviv University in 1951, earning the candidate of science degree and the docent title respectively in 1954 and 1956 from the same university: from 1951 on he worked at the Lviv Industrial Forestry Institute. In 1961 he became senior research fellow while 1962 he earned the "doktor nauk" degree from Moscow State University. In the 1970s–1980s A. I. Volpert became one of the leaders of the Russian Mathematical Chemistry scientific community. He finally joined Technion’s Faculty of Mathematics in 1993, doing his Aliyah in 1994. Work Index theory and elliptic boundary problems Vol'pert developed an effective algorithm for calculating the inde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kolmogorov's Criterion
In probability theory, Kolmogorov's criterion, named after Andrey Kolmogorov, is a theorem giving a necessary and sufficient condition for a Markov chain or continuous-time Markov chain to be stochastically identical to its time-reversed version. Discrete-time Markov chains The theorem states that an irreducible, positive recurrent, aperiodic Markov chain with transition matrix ''P'' is reversible if and only if its stationary Markov chain satisfies : p_ p_ \cdots p_ p_ = p_ p_ \cdots p_ p_ for all finite sequences of states : j_1, j_2, \ldots, j_n \in S . Here ''pij'' are components of the transition matrix ''P'', and ''S'' is the state space of the chain. That is, the chain-multiplication along any cycle is the same forwards and backwards. Example Consider this figure depicting a section of a Markov chain with states ''i'', ''j'', ''k'' and ''l'' and the corresponding transition probabilities. Here Kolmogorov's criterion implies that the product of probabilities when t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stationary Distribution
Stationary distribution may refer to: * and , a special distribution for a Markov chain such that if the chain starts with its stationary distribution, the marginal distribution of all states at any time will always be the stationary distribution. Assuming irreducibility, the stationary distribution is always unique if it exists, and its existence can be implied by positive recurrence of all states. The stationary distribution has the interpretation of the limiting distribution when the chain is irreducible and aperiodic. * The marginal distribution of a stationary process or stationary time series * The set of joint probability distributions of a stationary process or stationary time series In some fields of application, the term stable distribution is used for the equivalent of a stationary (marginal) distribution, although in probability and statistics the term has a rather different meaning: see stable distribution. Crudely stated, all of the above are specific cases of a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chain
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes. They provide the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distributions, and have found application in areas including Bayesian statistics, biology, chemistry, economics, fin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Process
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes. They provide the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distributions, and have found application in areas including Bayesian statistics, biology, chemistry, economics, finance, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bi-isotropic Material
In physics, engineering and materials science, a bi-isotropic material is an isotropic medium where the electric and magnetic flux densities are linearly coupled to both the electric and magnetic fields via scalar constitutive relations, including magnetoelectric coupling terms. A major subset of such materials, known as Pasteur media, are optically active: they can rotate the polarization of light in either refraction or transmission. This does not mean all materials with twist effect fall in the bi-isotropic class. The twist effect of the class of bi-isotropic materials is caused by the chirality and/or non- reciprocity of the structure of the media, in which the electric and magnetic field of an electromagnetic wave (or simply, light) interact in an unusual way. Definition For most materials, the electric field E and electric displacement field D (as well as the magnetic field B and inductive magnetic field H) are parallel to one another. These simple mediums are calle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
