Kinetic theory of nonequilibrium ensembles, irreversible thermodynamics, and generalized hydrodynamics. Volume 1, Nonrelativistic theories [electronic resource] / Byung Chan Eu.

Preface; Contents; 1 Introduction; References; Part I Nonrelativistic Theories; 2 Thermodynamic Theory of Irreversible Processes; 2.1 The Zeroth Law of Thermodynamics; 2.1.1 The Zeroth Law of Thermodynamics for Temperature; 2.1.2 The Zeroth Law of Thermodynamics Extended; 2.2 The First Law of Thermodynamics; 2.2.1 Internal Energy; 2.2.2 Work; 2.2.3 Local Forms of Evolution Equations; 2.3 The Second Law of Thermodynamics; 2.3.1 Carnot Theorem; 2.3.2 Clausius and Kelvin Principles; 2.3.3 Clausius Inequality; 2.3.4 Clausius Entropy; 2.3.5 Clausius
Duhem Inequality

2.4 Differential Form for Calortropy2.4.1 Local Differential Form for Calortropy; 2.4.2 Calortropy and Thermodynamic Relations; 2.5 Generalized Hydrodynamic Equations; 2.6 Irreversible Thermodynamics of Steady States; 2.7 Inclusion of Chemical Reactions; 2.8 Inclusion of Volume Transport; 2.9 Concluding Remarks; References; 3 Boltzmann Kinetic Equation; 3.1 Irreversible Processes in Dilute Monatomic Gases; 3.1.1 Conserved and Nonconserved Macroscopic Variables; 3.1.2 Collision Invariants; 3.1.3 Broken Time Reversal Symmetry and the Boltzmann Kinetic Equation

3.1.4 The H Theorem and Boltzmann Entropy3.2 Equilibrium Distribution Function; 3.2.1 Equilibrium Boltzmann Entropy; 3.2.2 Thermodynamic Correspondence and Equilibrium Gibbs Relation; 3.3 Evolution Equations for Macroscopic Variables; 3.3.1 Boltzmann Entropy Balance Equation; 3.3.2 Conservation Laws of Mass, Momentum, and Energy; 3.3.3 Evolution Equations for Nonconserved Variables; 3.4 Thermodynamics of Irreversible Processes in Dilute Monatomic Gases; 3.4.1 Functional Hypothesis for Distribution Functions; 3.4.2 Calotropy and the Second Law of Thermodynamics

3.4.3 Thermodynamic Correspondence3.5 Statistical Thermodynamics of Irreversible Processes; 3.5.1 Nonequilibrium Intensive Properties; 3.5.2 Nonequilibrium Partition Function; 3.5.3 Calortropy Production in Cumulant Expansion; 3.5.4 Cumulant Expansion for Dissipation Terms; 3.5.5 Collision Bracket Integrals; 3.5.6 Generalized Potentials; 3.5.7 Quasilinear Generalized Hydrodynamics and Transport Processes; 3.5.8 Linear Transport Processes; 3.5.9 A Model for Quasilinear Generalized Hydrodynamic Equations; 3.6 Relative Boltzmann Entropy; 3.6.1 Evolution Equation of Relative Boltzmann Entropy

3.6.2 Relative Boltzmann Entropy and Fluctuations3.6.3 Differential Equations for Fluctuations; 3.6.4 Stochastic Treatment of Fluctuations; 3.7 Concluding Remarks; References; 4 Equilibrium Ensemble Method; 4.1 Brief Review of Ensemble Methods; 4.2 Ensembles and Fundamental Postulates; 4.2.1 Canonical Ensemble; 4.2.2 Grand Canonical Ensemble; 4.3 Summary of the Gibbs Ensemble Theory; References; 5 Boltzmann-Like Equation for Moderately Dense Gases; 5.1 Extended Boltzmann Equation; 5.2 Cluster Expansion of the N-Particle Collision Operator; 5.3 Macroscopic Evolution Equations