Sur la mécanique statistique des phénomènes irréversibles III

Klein, G.

doi:10.1016/s0031-8914(53)80120-5

Cited by 54 publications

(29 citation statements)

References 4 publications

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“…However, the distribution of microscopic variables may nevertheless stay close to a maximum entropy distribution if the macroscopic variables change slowly enough such that the system remains close to a local equilibrium at all times (Prigogine 1949;Klein and Prigogine 1953;Nicolis and Prigogine 1977;De Groot and Mazur 1984;Goldstein and Lebowitz 2004).…”

Section: General Analysismentioning

confidence: 99%

Statistical Mechanics and the Evolution of Polygenic Quantitative Traits

2009

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The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nm . 1). We show how the method can be modified for small mutation rates (4Nm / 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.

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Section: General Analysismentioning

confidence: 99%

Statistical Mechanics and the Evolution of Polygenic Quantitative Traits

2009

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“…Описание неравновесных тепловых процессов в таких кристаллах является актуальной задачей физики твердого тела и востребовано во многих приложениях, связанных с нанотехнологиями. Удобной математической моделью для исследования тепловых процессов в твердых телах является гармонический кристалл (силы взаимодействия между частицами линейно зависят от их перемещений); такая модель часто используется в литературе [1][2][3][4][5][6][7][8][9][10][11][12][17][18][19][20][21][22][23][24][25][26]. Один из подходов к изучению таких кристаллов использует точные решения уравнений движения для описания статистических характеристик, таких как распределение вероятностей кинетической энергии или ее математическое ожидание ( " кинетическая температура") [3,6,[8][9][10]12,13,26].…”

Section: Introductionunclassified

Асимптотическое Описание Быстрых Тепловых Процессов В Скалярных Гармонических Решетках

Кориков¹

2020

Физика Твердого Тела

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Thermal processes in d-dimensional (d = 1,2) scalar harmonic lattices with simple structure are considered. The redistribution between the averaged kinetic and potential energies of particles after instantaneous thermal excitation is described. At times much longer than the characteristic period of atomic oscillations, the difference between the kinetic and potential energies oscillates with amplitude decreasing by a power law (typically, the exponent is -d/2). The frequencies of the oscillations are determined from the dispersion relation for the lattice. The above results can be generalized for scalar and vector lattices of complex structure and various dimensions. As an example, the oscillations of the kinetic tmperature in the two-dimensional hexagonal lattice (graphene lattice) are investigated.

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“…a set of particles forming a perfect lattice and interacting via linearized forces. An approach to thermal equilibrium in harmonic crystals is considered in many works [22][23][24][25][26][27][28][29][30][31][32]. In particular, in a pioneering paper by Klein & Prigogine [26], the behaviour of kinetic temperature, proportional to kinetic energy of thermal motion, in a one-dimensional harmonic chain with random initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Equilibration of energies in a two-dimensional harmonic graphene lattice

Berinskii

Kuzkin

2019

Phil. Trans. R. Soc. A.

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We study dynamical phenomena in a harmonic graphene (honeycomb) lattice, consisting of equal particles connected by linear and angular springs. Equations of in-plane motion for the lattice are derived. Initial conditions typical for molecular dynamic modelling are considered. Particles have random initial velocities and zero displacements. In this case, the lattice is far from thermal equilibrium. In particular, initial kinetic and potential energies are not equal. Moreover, initial kinetic energies (and temperatures), corresponding to degrees of freedom of the unit cell, are generally different. The motion of particles leads to equilibration of kinetic and potential energies and redistribution of kinetic energy among degrees of freedom. During equilibration, the kinetic energy performs decaying high-frequency oscillations. We show that these oscillations are accurately described by an integral depending on dispersion relation and polarization matrix of the lattice. At large times, kinetic and potential energies tend to equal values. Kinetic energy is partially redistributed among degrees of freedom of the unit cell. Equilibrium distribution of the kinetic energies is accurately predicted by the non-equipartition theorem. Presented results may serve for better understanding of the approach to thermal equilibrium in graphene. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

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Sur la mécanique statistique des phénomènes irréversibles III

Cited by 54 publications

References 4 publications

Statistical Mechanics and the Evolution of Polygenic Quantitative Traits

Statistical Mechanics and the Evolution of Polygenic Quantitative Traits

Асимптотическое Описание Быстрых Тепловых Процессов В Скалярных Гармонических Решетках

Equilibration of energies in a two-dimensional harmonic graphene lattice

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