Evans / Morriss / Craig Statistical Mechanics of Nonequilibrium Liquids

1. Auflage 2013
ISBN: 978-1-4832-6045-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 316 Seiten, Web PDF

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.

Autoren/Hrsg.

Evans, Denis J.

Morriss, Gary P.

Craig, D. P.

McWeeny, R.

Inhaltsverzeichnis

1;Front Cover;1
2;Statistical Mechanics of Nonequilibrium Liquids;4
3;Copyright Page;5
4;Table of Contents
;8
5;Preface;6
6;List of symbols;12
7;Chapter 1. Introduction;16
8;Chapter 2. Linear Irreversible Thermodynamics;26
8.1;2.1 The conservation equations;26
8.2;2.2 Entropy production;32
8.3;2.3 Curie's theorem;35
8.4;2.4 Non-Markovian constitutive relations: Viscoelasticity;43
8.5;References;47
9;Chapter 3. The Microscopic Connection;48
9.1;3.1 Classical Mechanics;48
9.2;3.2 Phase space;57
9.3;3.3 Distribution functions and the Liouville equation;59
9.4;3.4 Ergodicity, mixing and Lyapunov exponents;66
9.5;3.5 Equilibrium time correlation functions;71
9.6;3.6 Operator identities;76
9.7;3.7 The Irving–Kirkwood procedure
;79
9.8;3.8 Instantaneous microscopic representation o fluxes;86
9.9;3.9 The kinetic temperature;90
9.10;References;91
10;Chapter 4. The Green–Kubo Relations;92
10.1;4.1 The Langevin equation;92
10.2;4.2 Mori–Zwanzig Theory;96
10.3;4.3 Shear Viscosity;100
10.4;4.4 Green-Kubo relations for Navier-Stokes transport coefficients;105
10.5;References;107
11;Chapter 5. Linear Response Theory;110
11.1;5.1 Adiabatic linear response theory;110
11.2;5.2 Thermostats and equilibrium distribution functions;115
11.3;5.3 Isothermal linear response theory;126
11.4;5.4 The equivalence of thermostatted linear responses
;131
11.5;References;134
12;Chapter 6. Computer Simulation Algorithms;136
12.1;6.1 Introduction;136
12.2;6.2 Self-diffusion;143
12.3;6.3 Couette flow and shear viscosity;148
12.4;6.4 Thermostatting shear flows;161
12.5;6.5 Thermal conductivity;164
12.6;6.6 Norton ensemble methods;167
12.7;6.7 Constant-pressure ensembles;172
12.8;6.8 The constant-stress ensemble;175
12.9;References;182
13;Chapter 7. Nonlinear Response Theory;184
13.1;7.1 Kubo's form for the nonlinear response;184
13.2;7.2 Kawasaki distribution function;186
13.3;7.3 The transient time correlation function formalism;190
13.4;7.4 Trajectory mappings;194
13.5;7.5 Numerical results for the transient time correlation function;202
13.6;7.6 Differential response functions;207
13.7;7.7 Numerical results for the Kawasaki representation;213
13.8;7.8 The van kampen objection to linear response theory;217
13.9;References;225
14;Chapter 8. Time Dependent Response Theory;228
14.1;8.1 Introduction;228
14.2;8.2 Time evolution of phase variables;228
14.3;8.3 The inverse theorem;230
14.4;8.4 The associative law and composition theorem;233
14.5;8.5 Time evolution of the distribution function;235
14.6;8.6 Time ordered exponentials;236
14.7;8.7 Schrödinger and Heisenberg representations ;237
14.8;8.8 The Dyson equation;240
14.9;8.9 Relation between p- and f-propagators
;241
14.10;8.10 Time dependent response theory;242
14.11;8.11 Renormalization;245
14.12;8.12 Discussion;247
14.13;References;248
15;Chapter 9. Steady-State Fluctuations;250
15.1;9.1 Introduction;250
15.2;9.2 The specific heat;251
15.3;9.3 The compressibility and isobaric specific heat;256
15.4;9.4 Differential susceptibility;259
15.5;9.5 The inverse Burnett coefficients;263
15.6;References;265
16;Chapter 10. Towards a Thermodynamics of Steady States;266
16.1;10.1 Introduction;266
16.2;10.2 Chaotic dynamical systems;268
16.3;10.3 The characterization of chaos;279
16.4;10.4 Chaos in planar Couette flow;287
16.5;10.5 Green's expansion for the entropy;301
16.6;References;310
17;Index;312