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作者 Öttinger, Hans Christian
書名 Beyond Equilibrium Thermodynamics
出版項 Newy York : John Wiley & Sons, Incorporated, 2005
©2005
國際標準書號 9780471727910 (electronic bk.)
9780471666585
book jacket
版本 1st ed
說明 1 online resource (651 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
附註 Beyond Equilibrium Thermodynamics -- Contents -- Preface -- Acknowledgments -- Symbols and Notation -- 1 Introduction -- 1.1 To Be Expected, or Not to Be Expected -- 1.1.1 Thermodynamics and Rigor -- 1.1.2 Formulating Versus Deriving Irreversibility -- 1.1.3 Beyond Balance Equations -- 1.1.4 Guide Through the Book -- 1.2 GENERIC Framework -- 1.2.1 Fundamental Equations -- 1.2.2 Reversible and Irreversible Ancestors -- 1.2.3 Equilibrium Thermodynamics of Stationary States -- 1.2.4 Transformation of Variables -- 1.2.5 Fluctuations -- 1.2.6 Benefits of a Framework -- 1.2.7 Historical Context -- Part I Phenomenological Approach -- 2 Hydrodynamics -- 2.1 Balance Equations -- 2.1.1 Mass -- 2.1.2 Momentum -- 2.1.3 Energy -- 2.1.4 Entropy -- 2.1.5 Expressions for Fluxes -- 2.2 GENERIC Formulation -- 2.2.1 Energy and Entropy -- 2.2.2 Poisson Matrix -- 2.2.3 Friction Matrix -- 2.2.4 Fluctuating Hydrodynamics -- 2.2.5 Something is Missing -- 2.3 On Constructing GENERIC Building Blocks -- 2.3.1 Poisson Matrices -- 2.3.2 Friction Matrices -- 3 Linear Irreversible Thermodynamics -- 3.1 Thermodynamic Forces and Fluxes -- 3.1.1 Basic Concepts -- 3.1.2 Electric Field and Current -- 3.1.3 Transformation Behavior -- 3.1.4 Curie's Principle -- 3.1.5 Stationary States -- 3.2 Onsager-Casimir Relations -- 3.2.1 Bare and Dressed Symmetry -- 3.2.2 Thermoelectric Eflects -- 3.3 Paralyzing Criticism -- 4 Complex Fluids -- 4.1 Basic Rheological Properties -- 4.1.1 Linear Viscoelasticity -- 4.1.2 Nonlinear Material Behavior -- 4.2 Tensors and Scalars as Configurational Variables -- 4.2.1 Energy and Entropy -- 4.2.2 Poisson Matrix -- 4.2.3 Friction Matrix -- 4.2.4 Time-Evolution Equations -- 4.2.5 Summary of Inputs and Implications -- 4.2.6 Example: Dilute Polymer Solutions -- 4.2.7 Example: Pompon Model -- 4.3 Configurational Distribution Functions
4.3.1 Dumbbell Model of Polymer Solutions -- 4.3.2 Reptation Model of Polymer Melts -- 5 Relativistic Hydrodynamics -- 5.1 Prelude: A Tensor and a Vector as Variables -- 5.1.1 Energy and Entropy -- 5.1.2 Poisson Matrix -- 5.1.3 Friction Matrix -- 5.1.4 Time-Evolution Equations -- 5.1.5 Limit of Classical Hydrodynamics -- 5.1.6 Extended Irreversible Thermodynamics -- 5.2 Special Relativistic Hydrodynamics -- 5.2.1 Notation and Variables -- 5.2.2 Gradients of Energy and Entropy -- 5.2.3 Poisson and Friction Matrices -- 5.2.4 Covariant Field Equations -- 5.3 Covariant GENERIC Framework -- 5.3.1 Fundamental Equation -- 5.3.2 Degeneracy Requirements -- 5.4 Hydrodynamics in the Presence of Gravity -- 5.4.1 Notation and Variables -- 5.4.2 Reversible Contribution -- 5.4.3 Irreversible Contribution -- 5.4.4 Field Equations -- 5.5 Bulk Viscous Cosmology -- 5.5.1 Relativistic Thermodynamics -- 5.5.2 Input from Relativistic Boltzmann Gas -- 5.5.3 Model Predictions -- Part II Statistical Approach -- 6 Projection-Operator Method -- 6.1 Motivation of Basic Formulas -- 6.1.1 Notation of Classical Mechanics -- 6.1.2 Ensembles -- 6.1.3 Projection Operators -- 6.1.4 Atomistic Expressions for E, S, L, M -- 6.1.5 GENERIC Properties -- 6.1.6 Symmetries -- 6.2 Direct Approach -- 6.2.1 Exact Time-Evolution Equation -- 6.2.2 Markovian Approximation -- 6.2.3 Linear Response Theory -- 6.3 Probability Density Approach -- 6.3.1 Lifting Direct Results -- 6.3.2 GENERIC Building Blocks -- 6.3.3 Fluctuation-Dissipation Theorem -- 6.4 Relationship Between Coarse-Grained Levels -- 6.4.1 Static Properties -- 6.4.2 Friction Matrix -- 6.4.3 Generalizations -- 7 Kinetic Theory of Gases -- 7.1 Elementary Kinetic Theory -- 7.1.1 Model of a Rarefied Gas -- 7.1.2 Mean Free Path -- 7.1.3 Transport Coefficients -- 7.1.4 Boltzmann 's Equation -- 7.1.5 Differential Cross Section for Collisions
7.2 Projection-Operator Approach -- 7.2.1 Generalized Canonical Ensemble -- 7.2.2 Energy and Entropy -- 7.2.3 Poisson Matrix -- 7.2.4 Friction Matrix -- 7.2.5 Time-Evolution Equation -- 7.3 Chapman-Enskog Expansion -- 7.3.1 Some Remarks on Expansions -- 7.3.2 Chapman-Enskog Solution Technique -- 7.3.3 Transport Coefficients -- 7.4 Grad's Moment Method -- 7.4.1 Basic Idea -- 7.4.2 Thirteen-Moment Method -- 7.4.3 Structured Moment Method -- 7.5 Two-Particle Distribution Functions -- 7.5.1 Internal Energy -- 7.5.2 Rigorous Formula for the Pressure Tensor -- 8 Simulations -- 8.1 Simulation Philosophy -- 8.1.1 Understanding Through Simplicity -- 8.1.2 Relevance of Functional Forms -- 8.1.3 Overview of Simulation Techniques -- 8.2 Monte Carlo Simulations -- 8.2.1 Markov Chains -- 8.2.2 Importance Sampling and Detailed Balance -- 8.2.3 Example: Unentangled Polymer Melts -- 8.3 Brownian Dynamics -- 8.3.1 Stochastic Differential Equations -- 8.3.2 Example: Dilute Polymer Solutions -- 8.4 Molecular Dynamics -- 8.4.1 Expressions for lhe Friction Matrix -- 8.4.2 Friction Matrix for a Local Field Theory -- 8.4.3 Variostats and Multiplostats -- 8.4.4 Verlet- Type Integrators -- 8.4.5 Example: Rarefied Lennard-Jones Gas -- 8.4.6 Example: Entangled Polymer Melts -- Appendices -- Appendix A Crash-Course on Equilibrium Thermodynamics -- A.1 Approach and Scope -- A.2 Equilibrium States -- A.3 Basic Problem of Thermodynamics -- A.4 Thermodynamic Potentials -- A.5 Maxwell Relations and Stability Criteria -- A.6 Statistical Mechanics -- A.7 Perspectives -- Appendix B Mechanics and Geometry -- B.1 Basic Notions from Geometry -- B.2 Symplectic, Poisson, and Dirac Structures -- B.3 Reduction of Geometric Structures -- B.4 Body Tensors -- Appendix C Functional Derivatives -- C.1 Definitions and Examples -- C.2 Extremization of Functionals -- C.3 Incorporation of Constraints
Appendix D Quantum Systems -- D.1 Relevant Density Matrix -- D.2 Projection Operator -- D.3 Exact Time-Evolution Equation -- D.4 Markovian Approximation -- D.5 GENERIC Properties -- Appendix E List of Applications of Beyond-Equilibrium Thermodynamics -- E.1 Complex Fluids -- E.2 Relativistic Hydrodynamics and Cosmology -- E.3 Discrete Formulations of Hydrodynamics for Simulations -- E.4 Thermodynamically Guided Simulations -- Appendix F Solutions to Exercises -- References -- Author Index -- Subject Index
Beyond Equilibrium Thermodynamics fills a niche in the market by providing a comprehensive introduction to a new, emerging topic in the field. The importance of non-equilibrium thermodynamics is addressed in order to fully understand how a system works, whether it is in a biological system like the brain or a system that develops plastic. In order to fully grasp the subject, the book clearly explains the physical concepts and mathematics involved, as well as presenting problems and solutions; over 200 exercises and answers are included. Engineers, scientists, and applied mathematicians can all use the book to address their problems in modelling, calculating, and understanding dynamic responses of materials
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Öttinger, Hans Christian Beyond Equilibrium Thermodynamics Newy York : John Wiley & Sons, Incorporated,c2005 9780471666585
主題 Nonequilibrium thermodynamics
Electronic books
Alt Author Öttinger, Hans Christian
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