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Nonequilibrium Statistical Physics

This book presents a united approach to the statistical physics of systems near equilibrium: it brings out the profound unity of the laws which govern them and gathers together results usually fragmented in the literature.

Author : Noëlle Pottier

Release : 2010

Publisher : Oxford University Press

ISBN : 0199556881

File Size : 57.12 MB

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This book presents a united approach to the statistical physics of systems near equilibrium: it brings out the profound unity of the laws which govern them and gathers together results usually fragmented in the literature. It will be useful both as a textbook about irreversible phenomena and as a reference book for researchers.

Nonequilibrium and Irreversibility

Inventiones Mathematicae 29, 181–205 (1975) Gentile, G.: A large deviation
theorem for anosov flows. Forum Mathematicum 10, 89–118 (1998) Gallavotti, G.:
Fluctuation patterns and conditional reversibility in nonequilibrium systems.

Author : Giovanni Gallavotti

Release : 2014-06-10

Publisher : Springer

ISBN : 3319067583

File Size : 30.6 MB

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This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. A special feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending to support strongly the viewpoint that stationary states in or out of equilibrium can be described in a unified way. In this book it is the "chaotic hypothesis", which can be seen as an extension of the classical ergodic hypothesis to non equilibrium phenomena, that plays the central role. It is shown that SRB - often considered as a kind of mathematical playground with no impact on physical reality - has indeed a sound physical interpretation; an observation which to many might be new and a very welcome insight. Following this, many consequences of the chaotic hypothesis are analyzed in chapter 3 - 4 and in chapter 5 a few applications are proposed. Chapter 6 is historical: carefully analyzing the old literature on the subject, especially ergodic theory and its relevance for statistical mechanics; an approach which gives the book a very personal touch. The book contains an extensive coverage of current research (partly from the authors and his coauthors publications) presented in enough detail so that advanced students may get the flavor of a direction of research in a field which is still very much alive and progressing. Proofs of theorems are usually limited to heuristic sketches privileging the presentation of the ideas and providing references that the reader can follow, so that in this way an overload of this text with technical details could be avoided.

Non-Equilibrium Thermodynamics

Classic monograph treats irreversible processes and phenomena of thermodynamics: non-equilibrium thermodynamics.

Author : S. R. De Groot

Release : 2013-01-23

Publisher : Courier Corporation

ISBN : 0486153509

File Size : 66.68 MB

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Classic monograph treats irreversible processes and phenomena of thermodynamics: non-equilibrium thermodynamics. Covers statistical foundations and applications with chapters on fluctuation theory, theory of stochastic processes, kinetic theory of gases, more.

Nonequilibrium Thermodynamics

Nonequilibrium thermodynamics is based on the entropy production character of
nonequilibrium and irreversible processes and provides a ... In 1850, Clausius
introduced the concept of noncompensated heat as a measure of irreversibility.

Author : Yasar Demirel

Release : 2007-10-10

Publisher : Elsevier

ISBN : 9780080551364

File Size : 50.63 MB

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Natural phenomena consist of simultaneously occurring transport processes and chemical reactions. These processes may interact with each other and lead to instabilities, fluctuations, and evolutionary systems. This book explores the unifying role of thermodynamics in natural phenomena. Nonequilibrium Thermodynamics, Second Edition analyzes the transport processes of energy, mass, and momentum transfer processes, as well as chemical reactions. It considers various processes occurring simultaneously, and provides students with more realistic analysis and modeling by accounting possible interactions between them. This second edition updates and expands on the first edition by focusing on the balance equations of mass, momentum, energy, and entropy together with the Gibbs equation for coupled processes of physical, chemical, and biological systems. Every chapter contains examples and practical problems to be solved. This book will be effective in senior and graduate education in chemical, mechanical, systems, biomedical, tissue, biological, and biological systems engineering, as well as physical, biophysical, biological, chemical, and biochemical sciences. Will help readers in understanding and modelling some of the coupled and complex systems, such as coupled transport and chemical reaction cycles in biological systems Presents a unified approach for interacting processes - combines analysis of transport and rate processes Introduces the theory of nonequilibrium thermodynamics and its use in simultaneously occurring transport processes and chemical reactions of physical, chemical, and biological systems A useful text for students taking advanced thermodynamics courses

Extended Irreversible Thermodynamics

This is the 4th edition of the highly acclaimed monograph on Extended Irreversible Thermodynamics, a theory that goes beyond the classical theory of irreversible processes.

Author : David Jou

Release : 2010-09-16

Publisher : Springer Science & Business Media

ISBN : 9789048130740

File Size : 43.80 MB

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The fast progress in many areas of research related to non-equilibrium ther- dynamics has prompted us to write a fourth edition of this book. Like in the previous editions, our main concern is to open the subject to the widest au- ence, including students, teachers, and researchers in physics, chemistry, engine- ing, biology, and materials sciences. Our objective is to present a general view on several open problems arising in non-equilibrium situations, and to afford a wide perspective of applications illustrating their practical outcomes and con- quences. A better comprehension of the foundations is generally correlated to an increase of the range of applications, implying mutual feedback and cross fert- ization. Truly, thermodynamic methods are widely used in many areas of science but, surprisingly, the active dynamism of thermodynamics as a ?eld on its own is not suf?ciently perceived outside a relatively reduced number of specialized researchers. Extended irreversible thermodynamics (EIT) goes beyond the classical f- malisms based on the local equilibrium hypothesis; it was also referred to in an earlier publication by the authors (Lebon et al. 1992) as a thermodynamics of the third type, as it provides a bridge between classical irreversible thermodynamics and rational thermodynamics, enlarging at the same time their respective range of application. The salient feature of the theory is that the ?uxes are incorporated into the set of basic variables.

Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems

This book presents both the fundamentals and the major research topics in statistical physics of systems out of equilibrium.

Author : Werner Ebeling

Release : 2005

Publisher : World Scientific

ISBN : 9810213824

File Size : 29.64 MB

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This book presents both the fundamentals and the major research topics in statistical physics of systems out of equilibrium. It summarizes different approaches to describe such systems on the thermodynamic and stochastic levels, and discusses a variety of areas including reactions, anomalous kinetics, and the behavior of self-propelling particles.

Non-Equilibrium Entropy and Irreversibility

Again starting from one of the equilibrium states, a set of reproducible non-
equilibrium states is generated by the semigroup of evolutions defined by the
available time-dependent Hamiltonians. With a cyclic change in the Hamiltonian,
work is ...

Author : C. Lindblad

Release : 2001-11-30

Publisher : Springer Science & Business Media

ISBN : 9781402003202

File Size : 81.65 MB

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The problem of deriving irreversible thermodynamics from the re versible microscopic dynamics has been on the agenda of theoreti cal physics for a century and has produced more papers than can be digested by any single scientist. Why add to this too long list with yet another work? The goal is definitely not to give a gen eral review of previous work in this field. My ambition is rather to present an approach differing in some key aspects from the stan dard treatments, and to develop it as far as possible using rather simple mathematical tools (mainly inequalities of various kinds). However, in the course of this work I have used a large number of results and ideas from the existing literature, and the reference list contains contributions from many different lines of research. As a consequence the reader may find the arguments a bit difficult to follow without some previous exposure to this set of problems.

Kinetic Theory of Nonequilibrium Ensembles, Irreversible Thermodynamics, and Generalized Hydrodynamics

In this chapter, it is shown that the Boltzmann kinetic equation can be made use
of in order to construct the nonequilibrium canonical distribution function and
therewith formulate athermodynamic theory of irreversible transport processes in
a ...

Author : Byung Chan Eu

Release : 2016-08-02

Publisher : Springer

ISBN : 3319411470

File Size : 65.2 MB

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This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respect to macroscopic fluxes or thermodynamic forces. Both irreversible Boltzmann and generalized Boltzmann equations are used for deriving theories of irreversible transport equations and generalized hydrodynamic equations, which rigorously conform to the tenet. All observables described by the so-formulated theories therefore also strictly obey the tenet.

Non-Equilibrium Statistical Mechanics

Groundbreaking monograph by Nobel Prize winner for researchers and graduate students covers Liouville equation, anharmonic solids, Brownian motion, weakly coupled gases, scattering theory and short-range forces, general kinetic equations, ...

Author : Ilya Prigogine

Release : 2017-03-17

Publisher : Courier Dover Publications

ISBN : 0486815552

File Size : 24.14 MB

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Groundbreaking monograph by Nobel Prize winner for researchers and graduate students covers Liouville equation, anharmonic solids, Brownian motion, weakly coupled gases, scattering theory and short-range forces, general kinetic equations, more. 1962 edition.

Understanding Non-equilibrium Thermodynamics

Discover the many facets of non-equilibrium thermodynamics. The first part of this book describes the current thermodynamic formalism recognized as the classical theory. The second part focuses on different approaches.

Author : Georgy Lebon

Release : 2008-01-12

Publisher : Springer Science & Business Media

ISBN : 9783540742524

File Size : 83.73 MB

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Discover the many facets of non-equilibrium thermodynamics. The first part of this book describes the current thermodynamic formalism recognized as the classical theory. The second part focuses on different approaches. Throughout the presentation, the emphasis is on problem-solving applications. To help build your understanding, some problems have been analyzed using several formalisms to underscore their differences and their similarities.

Non-Equilibrium Thermodynamics in Multiphase Flows

Non-equilibrium thermodynamics is a general framework that allows the macroscopic description of irreversible processes. This book introduces non-equilibrium thermodynamics and its applications to the rheology of multiphase flows.

Author : Roberto Mauri

Release : 2012-11-08

Publisher : Springer Science & Business Media

ISBN : 9400754612

File Size : 34.36 MB

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Non-equilibrium thermodynamics is a general framework that allows the macroscopic description of irreversible processes. This book introduces non-equilibrium thermodynamics and its applications to the rheology of multiphase flows. The subject is relevant to graduate students in chemical and mechanical engineering, physics and material science. This book is divided into two parts. The first part presents the theory of non-equilibrium thermodynamics, reviewing its essential features and showing, when possible, some applications. The second part of this book deals with how the general theory can be applied to model multiphase flows and, in particular, how to determine their constitutive relations. Each chapter contains problems at the end, the solutions of which are given at the end of the book. No prior knowledge of statistical mechanics is required; the necessary prerequisites are elements of transport phenomena and on thermodynamics. “The style of the book is mathematical, but nonetheless it remains very readable and anchored in the physical world rather than becoming too abstract. Though it is up-to-date and includes recent important developments, there is a lot of classical material in the book, albeit presented with unprecedented clarity and coherence. The first six chapters are actually a very good introduction to the theory underlying many phenomena in soft matter physics, beyond the focus on flow and transport of the later chapters of the book.” Prof Richard A.L. Jones FRS, Pro-Vice-Chancellor for Research and Innovation, University of Sheffield

Chemical Thermodynamics

This book aims to introduce to advanced undergraduate students and graduate students the fundamental ideas and notions of the first and second laws of thermodynamics in a manner unavailable in the usual textbooks on the subject of ...

Author : Byung Chan Eu

Release : 2010-08-06

Publisher : World Scientific Publishing Company

ISBN : 9814365181

File Size : 80.47 MB

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Thermodynamics is an ever evolving subject. This book aims to introduce to advanced undergraduate students and graduate students the fundamental ideas and notions of the first and second laws of thermodynamics in a manner unavailable in the usual textbooks on the subject of thermodynamics. For example, it treats the notions of unavailable work, compensated and uncompensated heats, and dissipation, which make it possible to formulate the thermodynamic laws in more broadened forms than those in the conventional treatment of equilibrium thermodynamics. It thus strives to prepare students for more advanced subjects of irreversible processes, which are encountered in our everyday scientific activities. In addition, it also aims to provide them with functional and practical knowledge of equilibrium chemical thermodynamics of reversible processes in real fluids. It discusses temperature, work and heat, thermodynamic laws, equilibrium conditions and thermodynamic stability, thermodynamics of reversible processes in gases and liquids, in surfaces, chemical equilibria, reversible processes in electrolyte solutions and dielectrics in static electric and magnetic fields. A couple of examples for irreversible processes associated with fluid flows and chemical pattern formation and wave propagations are discussed as examples for applications of broader treatments of the thermodynamic laws in the realm of irreversible phenomena.

Statistical Mechanics of Nonequilibrium Liquids

Statistical Mechanics of Nonequilibrium Liquids deals with theoretical rheology. The book discusses nonlinear response of systems and outlines the statistical mechanical theory.

Author : Denis J. Evans

Release : 2013-10-22

Publisher : Elsevier

ISBN : 1483260453

File Size : 86.23 MB

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Statistical Mechanics of Nonequilibrium Liquids deals with theoretical rheology. The book discusses nonlinear response of systems and outlines the statistical mechanical theory. In discussing the framework of nonequilibrium statistical mechanics, the book explains the derivation of a nonequilibrium analogue of the Gibbsian basis for equilibrium statistical mechanics. The book reviews the linear irreversible thermodynamics, the Liouville equation, and the Irving-Kirkwood procedure. The text then explains the Green-Kubo relations used in linear transport coefficients, the linear response theory, the isothermal linear response theory, as well as the equivalence of thermostatted linear responses. The book also describes how thermostatted linear mechanical response of many-body systems can be related to equilibrium fluctuations. The text explains the procedure for calculating the linear Navier-Stokes transport coefficients through computer simulation algorithms. The book also discusses the van Kampen objection to linear response theory, the steady-state fluctuations, and the thermodynamics of steady states. The text will prove valuable for researchers in molecular chemistry, scientists, and academicians involved in advanced physics.

Nonequilibrium Statistical Physics

Authored by a well-known expert in the field of nonequilibrium statistical physics, this book is a coherent presentation of the subject suitable for masters and PhD students, as well as postdocs in physics and related disciplines.

Author : Gerd Röpke

Release : 2013-03-01

Publisher : John Wiley & Sons

ISBN : 3527670572

File Size : 51.27 MB

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Authored by a well-known expert in the field of nonequilibrium statistical physics, this book is a coherent presentation of the subject suitable for masters and PhD students, as well as postdocs in physics and related disciplines. Starting from a general discussion of irreversibility and entropy, the method of nonequilibrium statistical operator is presented as a general concept. Stochastic processes are introduced as a necessary prerequisite to describe the evolution of a nonequilibrium state. Different standard approaches such as master equations, kinetic equations and linear response theory, are derived after special assumptions. This allows for an insight into the problems of nonequilibrium physics, a discussion of the limits of the approaches, and suggestions for improvements. The method of thermodynamic Green's function is outlined that allows for the systematic quantum statistical treatment of many-body systems. Applications and typical examples are given, as well as fully worked problems.

Statistical Mechanics and Dynamics of Driven and Active Systems

In this thesis, we work towards advancing the thermodynamic theory of non-equilibrium phenomena by studying models of driven-diffusive systems, growth processes, and active matter.

Author : Katherine Klymko

Release : 2018

Publisher :

ISBN :

File Size : 45.43 MB

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Systems driven out of equilibrium display a rich variety of patterns and surprising response behaviors. There exist different types of non-equilibrium processes, for instance a system that has been prepared in a non-Boltzmann initial state and is relaxing back to equilibrium, or a system that adopts a non-equilibrium steady state distribution when it is driven by an external field. In these different cases, the main characteristic that distinguishes these systems as non-equilibrium is that they are constantly dissipating heat, or likewise producing entropy. This entropy production is often the starting point for developing a systematic theory to describe such non-equilibrium processes. Entropy production can be related to the irreversible processes occurring within a system. Particularly strong statements can be made about non-equilibrium systems when a local equilibrium assumption can be made, that is, when smaller subsets of a large system can be considered to be in equilibrium. This turns out to be justified for a wide variety of systems under different conditions. When this holds, the entropy production can be written as a generalized thermodynamic force (often the gradient of some intensive variable of the system) multiplied by a flux. When the thermodynamic force is small, the fluxes can be written as linear combinations of the thermodynamic forces, connected by response coefficients–this is known as linear irreversible thermodynamics. The full extension of equilibrium thermodynamic concepts to dissipative processes beyond this linear regime, including the development of microscopic principles justifying irreversible thermodynamic theories (as equilibrium statistical mechanics justifies equilibrium thermodynamics), is still a work in progress. In this thesis, we work towards advancing the thermodynamic theory of non-equilibrium phenomena by studying models of driven-diffusive systems, growth processes, and active matter. We use developments from stochastic thermodynamics, large deviation theory, and irreversible thermodynamics to characterize the non-equilibrium phases and properties exhibited by these systems. We question to what extent equilibrium approximations are valid for predicting pattern formation in these systems and whether there exist general unifying features describing these non-equilibriums processes. In the process we develop trajectory sampling methods to investigate the statistics of dynamical order parameters distinguishing these phases. We show how the first and second laws of thermodynamics, including consistent expressions for entropy production, can be extended to active systems, where microscopic reversibility is broken at the level of individual particles. Additionally we derive fluctuation relations, exact analytical results for the fluctuations of entropy production in the form of equalities, for the entropy production in active systems. We also extend the Irving-Kirkwood procedure to active systems, deriving the balance laws of mass, momentum, and energy. Consequently we obtain expressions for the stress and couple stress tensors in the system as functions of the microscopic variables. This provides a foundation to extend the framework of irreversible thermodynamics to active systems.

Mathematical Theory of Nonequilibrium Steady States

This volume provides a systematic mathematical exposition of the conceptual problems of nonequilibrium statistical physics, such as entropy production, irreversibility, and ordered phenomena.

Author : Da-Quan Jiang

Release : 2004-02-12

Publisher : Springer Science & Business Media

ISBN : 9783540206118

File Size : 21.76 MB

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This volume provides a systematic mathematical exposition of the conceptual problems of nonequilibrium statistical physics, such as entropy production, irreversibility, and ordered phenomena. Markov chains, diffusion processes, and hyperbolic dynamical systems are used as mathematical models of physical systems. A measure-theoretic definition of entropy production rate and its formulae in various cases are given. It vanishes if and only if the stationary system is reversible and in equilibrium. Moreover, in the cases of Markov chains and diffusion processes on manifolds, it can be expressed in terms of circulations on directed cycles. Regarding entropy production fluctuations, the Gallavotti-Cohen fluctuation theorem is rigorously proved.

Dynamical Systems and Irreversibility

However, the nonequilibrium conditions created by the absorbing boundaries
lead to a small difference between the KS entropy and the sum of positive
Lyapunov exponents. This difference is of the order of the inverse of a
hydrodynamic time ...

Author : Ioannis Antoniou

Release : 2003-10-17

Publisher : John Wiley & Sons

ISBN : 0471234273

File Size : 24.17 MB

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Leading research, perspectives, and analysis of dynamical systems and irreversibility Edited by Nobel Prize winner Ilya Prigogine and renowned authority Stuart A. Rice, the Advances in Chemical Physics series provides a forum for critical, authoritative evaluations in every area of the discipline. In a format that encourages the expression of individual points of view, experts in the field present comprehensive analyses of subjects of interest. Volume 122 collects papers from the XXI Solvay Conference on Physics, dedicated to the exploration of "Dynamical Systems and Irreversibility." Ioannis Antoniou, Deputy Director of the International Solvay Institutes for Physics and Chemistry, edits and assembles this cutting-edge research, including articles such as "Non-Markovian Effects in the Standard Map," "Harmonic Analysis of Unstable Systems," "Age and Age Fluctuations in an Unstable Quantum System," and discussion of many more subjects. Advances in Chemical Physics remains the premier venue for presentations of new findings in its field.

Nonequilibrium Nondissipative Thermodynamics

2.2.1 Irreversibility of Change with Time The introduction of the concept of the
entropy and the entropy increase principle is a very important event in classical
thermodynamics. The increase of the total entropy for isolated systems is
irreversible ...

Author : Ji-Tao Wang

Release : 2002-03-07

Publisher : Springer Science & Business Media

ISBN : 9783540428022

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This book introduces a new and successful concept for thermodynamics: nonequilibrium phase diagrams. This concept has been successfully applied to diamond synthesis. The book goes on to demonstrate how these diagrams lead to a complete new systematization of modern thermodynamics.

Non-Dissipative Effects in Nonequilibrium Systems

This book introduces and discusses both the fundamental aspects and the measurability of applications of time-symmetric kinetic quantities, outlining the features that constitute the non-dissipative branch of non-equilibrium physics.

Author : Christian Maes

Release : 2017-09-20

Publisher : Springer

ISBN : 3319677802

File Size : 58.57 MB

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This book introduces and discusses both the fundamental aspects and the measurability of applications of time-symmetric kinetic quantities, outlining the features that constitute the non-dissipative branch of non-equilibrium physics. These specific features of non-equilibrium dynamics have largely been ignored in standard statistical mechanics texts. This introductory-level book offers novel material that does not take the traditional line of extending standard thermodynamics to the irreversible domain. It shows that although stationary dissipation is essentially equivalent with steady non-equilibrium and ubiquitous in complex phenomena, non-equilibrium is not determined solely by the time-antisymmetric sector of energy-entropy considerations. While this should not be very surprising, this book provides timely, simple reminders of the role of time-symmetric and kinetic aspects in the construction of non-equilibrium statistical mechanics.