File Name: an introduction to stochastic processes and nonequilibrium statistical physics .zip
Online via Zoom link. Summary: Suppose someone gave you a terabyte of data on an epidemic. What are the theoretical concepts you need to know in order to understand collective behaviour in such a system? Technological breakthroughs in biology and the social sciences now give unprecedented access to microscopic states of non-equilibrium systems, requiring a rethinking about our approaches to understanding collective degrees of freedom in complex systems. In this lecture, we will take an interdisciplinary perspective on the concepts necessary to identify and understand collective order in space and time.
Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green—Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations continuous versus discontinuous is reflected in the mathematical structure of the phenomenological equations. Phenomenological evolution equations with a thermodynamic structure can be enhanced by adding fluctuations.
This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluctuations around metastable and unstable points are given.
Reichl: A modern course in statisitical physics. Wiley-Interscience, New York Wilde and S. Singh: Statistical mechanics. Fundamentals and modern applications. Wiley, New York Gardiner: Handbook of stochastic methods for physics, chemistry, and the natural sciences.
Path integrals and perturbation theory for stochastic processes. We review and extend the formalism introduced by Peliti, that maps a Markov process to a path-integral representation. After developing the mapping, we apply it to some illustrative examples: the simple decay process, the birth-and-death process, and the Malthus-Verhulst process. In the fi rst two cases we show how to obtain the exact probability generating function using the path integral. We show how to implement a diagrammatic perturbation theory for processes that do not admit an exact solution. Analysis of a set of coupled Malthus-Verhulst processes on a lattice leads, in the continuum limit, to a field theory for directed percolation and allied models.
This book deals with the basic principles and techniques of nonequilibrium statistical mechanics. The importance of this subject is growing rapidly in view of the advances being made, both experimentally and theoretically, in statistical physics, chemical physics, biological physics, complex systems and several other areas. The presentation of topics is quite self-contained, and the choice of topics enables the student to form a coherent picture of the subject. The approach is unique in that classical mechanical formulation takes center stage. The book is of particular interest to advanced undergraduate and graduate students in engineering departments. Springer Professional. Back to the search result list.
Probabilities. van Kampen, N. G., , Stochastic Processes in Physics and Chemistry (Elsevier Sci- ence B. V. rather general and not restricted to non-equilibrium statistical mechanics, although some We start this section by considering the probability density function (PDF) Pa (x), which, in.
Opening Chapter 1. In the first chapter the reader can find the basic ingredients of elementary kinetic theory and of the mathematical approach to discrete and continuous stochastic processes. All that is necessary to establish a solid ground for nonequilibrium processes concerning the time evolution of physical systems subject to a statistical description. In fact, from the first sections we discuss problems where we deal with the time evolution of average quantities, like in the elementary random walk model of diffusion. We also illustrate the bases of transport phenomena that allow us to introduce the concept of transport coefficients, that will be reconsidered later in the framework of a more general theory see Chap.
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Nonequilibrium situations are far more common in nature than equilibrium ones. This course gives an introduction to the common ideas and different approaches for studying systems in statistical mechanics that are not in equilibrium, i. We begin with a review of the origin of irreversibility and the second law of thermodynamics, which are at the foundations of equilibrium statistical mechanics. Then various different techniques for studying non-equilibrium situations follows, which treat the problem on different levels of detail. The main part of the course considers effective descriptions in terms of stochastic processes, closely related to simple random walk problems.
Немного? - Глаза Бринкерхоффа сузились. - У Стратмора стол ломится от заказов. Вряд ли он позволил бы ТРАНСТЕКСТУ простаивать целый уик-энд. - Хорошо, хорошо. - Мидж вздохнула.
О, Дэвид… у меня нет слов. - Скажи. Она отвернулась.
Выдержав долгую паузу, Мидж шумно вздохнула. - Возможны ли другие варианты. - Конечно.
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