Beyond Equilibrium Thermodynamics by Hans Christian Öttinger

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Beyond Equilibrium Thermodynamics

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Contents of Beyond Equilibrium Thermodynamics

  • Symbols and Notation
  • Introduction
  • To Be Expected, or Not to Be Expected
  • Thermodynamics and Rigor
  • Formulating Versus Deriving Irreversibility
  • Beyond Balance Equations
  • Guide Through the Book
  • Fundamental Equations
  • Reversible and Jrreversible Ancestors
  • Equilibrium Thermodynamics of Stationary States
  • Transformation of Variables
  • Fluctuations
  • Benefits of a Frtzmework
  • Historical Context
  • GENERIC Framework
  • Part I Phenomenological Approach
  • Hydrodynamics
  • Balance Equations
  • Mass
  • Momentum
  • Energy
  • Entropy
  • Expressions for Fluxes
  • GENERIC Formulation
  • Energy and Entropy
  • Poisson Matrix
  • Friction Matrix
  • Fluctuating Hydrodynamics
  • Something is Missing
  • On Constructing GENERIC Building Blocks
  • Poisson Matrices
  • Friction Matrices
  • Linear Irreversible Thermodynamics
  • Thermodynamic Forces and Fluxes
  • Basic Concepts
  • Electric Field and Current
  • Transformation Behavior
  • Curie ‘s Principle
  • Stationary States
  • Bare and Dressed Symmetry
  • Thermoelectric Eflects
  • Onsager-Casimir Relations
  • Paralyzing Criticism
  • Complex Fluids
  • Basic Rheological Properties
  • Linear Viscoelasticity
  • Nonlinear Material Behavior
  • Tensors and Scalars as Configurational Variables
  • Energy and Entropy
  • Poisson Matrix
  • Friction Matrix
  • Time-Evolution Equations
  • Summary of Inputs and Implications
  • Example: Dilute Polymer Solutions
  • Example: Pompon Model
  • Conjigurational Distribution Functions
  • Dumbbell Model of Polymer Solutions
  • Reptation Model of Polymer Melts
  • Relativistic Hydrodynamics
  • Prelude: A Tensor and a Vector as Variables
  • Energy and Entropy
  • Poisson Matrix
  • Friction Matrix
  • Time-Evolution Equations
  • Special Relativistic Hydrodynamics
  • Notation and Variables
  • Poisson and Friction Matrices
  • Covariant Field Equations
  • Covariant GENERIC Framework
  • Fundamental Equation
  • Degeneracy Requirements
  • Hydrodynamics in the Presence of Gravity
  • I Notation and Variables
  • Reversible Contribution
  • Irreversible Contribution
  • Field Equations
  • Relativistic Thermodynamics
  • Model Predictions
  • Limit of Classical Hydrodynamics
  • Extended Irreversible Thermodynamics
  • Gradients of Energy and Entropy
  • Bulk viscous Cosmology
  • Input from Relativistic Boltzmann Gas
  • Part N Statistical Approach
  • Projection-Operator Method
  • Motivation of Basic Formulas
  • Ensembles
  • Projection Operators
  • GENERIC Properties
  • Symmetries
  • Exact Time-Evolution Equation
  • Markovian Approximation
  • Linear Response Theory
  • Lifing Direct Results
  • GENERIC Building Blocks
  • Fluctuation-Dissipation Theorem
  • Relationship Between Coarse-Grained Levels
  • Static Properties
  • Friction Matrix
  • Generalizations
  • Notation of Classical Mechanics
  • Atomistic Expressions for E, S, L, M
  • Direct Approach
  • Probability Density Approach
  • Kinetic Theory of Gases
  • Elementary Kinetic Theory
  • Mean Free Path
  • Transport CoefJicients
  • Boltzmann ‘s Equation
  • Differential Cross Section for Collisions
  • Generalized Canonical Ensemble
  • Energy and Entropy
  • Poisson Matrix
  • Friction Matrix
  • Time-Evolution Equation
  • Chapman-Enskog Expansion
  • Some Remarks on Expansions
  • Model of a Rarefied Gas
  • Projection-Operator Approach
  • Chapman-Enskog Solution Technique
  • Transport CoefJicients
  • Grad’s Moment Method
  • Basic Idea
  • Thirteen-Moment Method
  • Structured Moment Method
  • Internal Energy
  • Two-Particle Distribution Functions
  • Rigorous Formula for the Pressure Tensor
  • Simulations
  • Simulation Philosophy
  • Understanding Through Simplicity
  • Relevance of Functional Forms
  • Overview of Simulation Techniques
  • Markov Chains
  • Example: Unentangled Polymer Melts
  • Stochastic Differential Equations
  • Example: Dilute Polymer Solutions
  • Expressions for lhe Friction Matrix
  • Friction Matrix for a Local Field Theory
  • Variostats and Multiplostats
  • Verlet- Type Integrators
  • Example: Rarefied Lennard-Jones Gas
  • Example: Entangled Polymer Melts
  • Monte Carlo Simulations
  • Importance Sampling and Detailed Balance
  • Brownian Dynamics
  • Molecular Dynamics
  • Appendices
  • Appendix A Crash-Course on Equilibrium Thermodynamics
  • Approach and Scope
  • Equilibrium States
  • Basic Problem of Thermodynamics
  • Thermodynamic Potentials
  • Statistical Mechanics
  • Perspectives
  • Maxwell Relations and Stability Criteria
  • Appendix B Mechanics and Geometry
  • Basic Notions from Geometry
  • Symplectic, Poisson, and Dirac Structures
  • Reduction of Geometric Structures
  • Body Tensors
  • Appendix C Functional Derivatives
  • Definitions and Examples
  • Extremization of Functionals
  • Incorporation of Constraints
  • Appendix D Quantum Systems
  • Relevant Density Matrix
  • Projection Operator
  • Exact Time-Evolution Equation
  • Markovian Approximation
  • GENERIC Properties
  • Appendix E List of Applications of Beyond-Equilibrium
  • Thermodynamics
  • Complex Fluids
  • Relativistic Hydrodynamics and Cosmology
  • Thermodynamically Guided Simulations
  • Discrete Formulations of Hydrodynamics for
  • Simulations

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