Stochastic Dynamics Out of Equilibrium

Stochastic Dynamics Out of Equilibrium
Title Stochastic Dynamics Out of Equilibrium PDF eBook
Author Giambattista Giacomin
Publisher Springer
Pages 654
Release 2019-06-30
Genre Mathematics
ISBN 3030150968

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Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas.

Stochastic Dynamics and Irreversibility

Stochastic Dynamics and Irreversibility
Title Stochastic Dynamics and Irreversibility PDF eBook
Author Tânia Tomé
Publisher Springer
Pages 402
Release 2014-11-26
Genre Science
ISBN 331911770X

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This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomena both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of physics and chemistry and for those interested in stochastic dynamics. It provides, by means of examples and problems, a comprehensive and detailed explanation of the theory and its applications.

Statistical Dynamics: Matter Out Of Equilibrium

Statistical Dynamics: Matter Out Of Equilibrium
Title Statistical Dynamics: Matter Out Of Equilibrium PDF eBook
Author Radu Balescu
Publisher World Scientific
Pages 340
Release 1997-04-19
Genre Science
ISBN 1783262613

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In the first part of this book, classical nonequilibrium statistical mechanics is developed. Starting from the Hamiltonian dynamics of the molecules, it leads through the irreversible kinetic equations to the level of fluid mechanics. For simple systems, all the transport coefficients are determined by the molecular properties.The second part of the book treats complex systems that require a more extensive use of statistical concepts. Such problems, which are at the forefront of research, include: continuous time random walks, non-Markovian diffusion processes, percolation and related critical phenomena, transport on fractal structures, transport and deterministic chaos. These “strange transport processes” differ significantly from the usual (diffusive) transport. Their inclusion in a general treatise on statistical mechanics is a special feature of this invaluable book./a

Statistical Dynamics

Statistical Dynamics
Title Statistical Dynamics PDF eBook
Author R. F. Streater
Publisher Imperial College Press
Pages 393
Release 2009
Genre Science
ISBN 1848162448

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How can one construct dynamical systems obeying the first and second laws of thermodynamics: mean energy is conserved and entropy increases with time? This book answers the question for classical probability (Part I) and quantum probability (Part II). A novel feature is the introduction of heat particles which supply thermal noise and represent the kinetic energy of the molecules. When applied to chemical reactions, the theory leads to the usual nonlinear reaction-diffusion equations as well as modifications of them. These can exhibit oscillations, or can converge to equilibrium.In this second edition, the text is simplified in parts and the bibliography has been expanded. The main difference is the addition of two new chapters; in the first, classical fluid dynamics is introduced. A lattice model is developed, which in the continuum limit gives us the Euler equations. The five Navier-Stokes equations are also presented, modified by a diffusion term in the continuity equation. The second addition is in the last chapter, which now includes estimation theory, both classical and quantum, using information geometry.

Critical Dynamics

Critical Dynamics
Title Critical Dynamics PDF eBook
Author Uwe C. Täuber
Publisher Cambridge University Press
Pages 529
Release 2014-03-06
Genre Science
ISBN 0521842239

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A comprehensive and unified introduction to describing and understanding complex interacting systems.

An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics

An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics
Title An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics PDF eBook
Author Horacio S. Wio
Publisher World Scientific Publishing Company Incorporated
Pages 217
Release 1994-01-01
Genre Science
ISBN 9789810215712

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Statistical Thermodynamics of Nonequilibrium Processes

Statistical Thermodynamics of Nonequilibrium Processes
Title Statistical Thermodynamics of Nonequilibrium Processes PDF eBook
Author Joel Keizer
Publisher Springer Science & Business Media
Pages 517
Release 2012-12-06
Genre Science
ISBN 1461210542

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The structure of the theory ofthermodynamics has changed enormously since its inception in the middle of the nineteenth century. Shortly after Thomson and Clausius enunciated their versions of the Second Law, Clausius, Maxwell, and Boltzmann began actively pursuing the molecular basis of thermo dynamics, work that culminated in the Boltzmann equation and the theory of transport processes in dilute gases. Much later, Onsager undertook the elucidation of the symmetry oftransport coefficients and, thereby, established himself as the father of the theory of nonequilibrium thermodynamics. Com bining the statistical ideas of Gibbs and Langevin with the phenomenological transport equations, Onsager and others went on to develop a consistent statistical theory of irreversible processes. The power of that theory is in its ability to relate measurable quantities, such as transport coefficients and thermodynamic derivatives, to the results of experimental measurements. As powerful as that theory is, it is linear and limited in validity to a neighborhood of equilibrium. In recent years it has been possible to extend the statistical theory of nonequilibrium processes to include nonlinear effects. The modern theory, as expounded in this book, is applicable to a wide variety of systems both close to and far from equilibrium. The theory is based on the notion of elementary molecular processes, which manifest themselves as random changes in the extensive variables characterizing a system. The theory has a hierarchical character and, thus, can be applied at various levels of molecular detail.