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.