Statistical Mechanics of Nonequilibrium Liquids - 1st Edition - ISBN: 9780122440908, 9781483260457

Statistical Mechanics of Nonequilibrium Liquids

1st Edition

Authors: Denis J. Evans Gary P. Morriss
Editors: D. P. Craig R. McWeeny
eBook ISBN: 9781483260457
Imprint: Academic Press
Published Date: 17th July 1990
Page Count: 316
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Description

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.

Table of Contents


Preface

List of symbols

1 Introduction

2 Linear Irreversible Thermodynamics

2.1 The Conservation Equations

2.2 Entropy Production

2.3 Curie'S Theorem

2.4 Non-Markovian Constitutive Relations: Viscoelasticity

References

3 The Microscopic Connection

3.1 Classical Mechanics

3.2 Phase Space

3.3 Distribution Functions and the Liouville Equation

3.4 Ergodicity, Mixing and Lyapunov Exponents

3.5 Equilibrium Time Correlation Functions

3.6 Operator Identities

3.7 The Irving-Kirkwood Procedure

3.8 Instantaneous Microscopic Representation of Fluxes

3.9 The Kinetic Temperature

References

4 The Green-Kubo Relations

4.1 The Langevin Equation

4.2 Mori-Zwanzig Theory

4.3 Shear Viscosity

4.4 Green-Kubo Relations for Navier-Stokes Transport Coefficients

References

5 Linear Response Theory

5.1 Adiabatic Linear Response Theory

5.2 Thermostats and Equilibrium Distribution Functions

5.3 Isothermal Linear Response Theory

5.4 The Equivalence of the Thermostatted Linear Responses

References

6 Computer Simulation Algorithms

6.1 Introduction

6.2 Self-Diffusion

6.3 Couette Flow and Shear Viscosity

6.4 Thermostatting Shear Flows

6.5 Thermal Conductivity

6.6 Norton Ensemble Methods

6.7 Constant-Pressure Ensembles

6.8 The Constant-Stress Ensemble

References

7 Nonlinear Response Theory

7.1 Kubo'S Form for the Nonlinear Response

7.2 Kawasaki Distribution Function

7.3 The Transient Time Correlation Function Formalism

7.4 Trajectory Mappings

7.5 Numerical Results for the Transient Time Correlation Function

7.6 Differential Response Functions

7.7 Numerical Results for the Kawasaki Representation

7.8 The Van Kampen Objection to Linear Response Theory

References

8 Time Dependent Response Theorya

8.1 Introduction

8.2 Time Evolution of Phase Variables

8.3 The Inverse Theorem

8.4 The Associative Law and Composition Theorem

8.5 Time Evolution of the Distribution Function

8.6 Time Ordered Exponentials

8.7 Schrodinger and Heisenberg Representations

8.8 The Dyson Equation

8.9 Relation Between P- and f-Propagators

8.10 Time Dependent Response Theory

8.11 Renormalization

8.12 Discussion

References

9 Steady-State Fluctuations

9.1 Introduction

9.2 The Specific Heat

9.3 The Compressibility and Isobaric Specific Heat

9.4 Differential Susceptibility

9.5 The Inverse Burnett Coefficients

References

10 Towards a Thermodynamics of Steady States

10.1 Introduction

10.2 Chaotic Dynamical Systems

10.3 The Characterization of Chaos

10.4 Chaos in Planar Couette Flow

10.5 Green's Expansion for the Entropy

References

Index


Details

No. of pages:
316
Language:
English
Copyright:
© Academic Press 1990
Published:
Imprint:
Academic Press
eBook ISBN:
9781483260457

About the Author

Denis J. Evans

Gary P. Morriss

About the Editor

D. P. Craig

R. McWeeny

Affiliations and Expertise

Universita di pisa

Ratings and Reviews