Fundamentals of Classical Statistical Thermodynamics

1 INTRODUCTION
 
2 INTRODUCTION TO TIME-REVERSIBLE, THERMOSTATTED DYNAMICAL SYSTEMS, AND STATISTICAL MECHANICAL ENSEMBLES
2.1 Time Reversibility in Dynamical Systems
2.2 Introduction to Time-Reversible, Thermostatted Dynamical Systems
2.3 Example: Homogeneously Thermostatted SLLOD Equations for Planar Couette Flow
2.4 Phase Continuity Equation
2.5 Lyapunov Instability and Statistical Mechanics
2.6 Gibbs Entropy in Deterministic Nonequilibrium Macrostates
2.A Appendix: Phase Space Expansion Calculation
 
3 THE EVANS-SEARLES FLUCTUATION THEOREM
3.1 The Transient Fluctuation Theorem
3.2 Second Law Inequality
3.3 Nonequilibrium Partition Identity
3.4 Integrated Fluctuation Theorem
3.5 Functional Transient Fluctuation Theorem
3.6 The Covariant Dissipation Function
3.7 The Definition of Equilibrium
3.8 Conclusion
 
4 THE DISSIPATION THEOREM
4.1 Derivation of the Dissipation Theorem
4.2 Equilibrium Distributions are Preserved by Their Associated Dynamics
4.3 Broad Characterization of Nonequilibrium Systems: Driven, Equilibrating, and T-Mixing Systems
 
5 EQUILIBRIUM RELAXATION THEOREMS
5.1 Introduction
5.2 Relaxation toward Mixing Equilibrium: The Umbrella Sampling Approximation
5.3 Relaxation of Autonomous Hamiltonian Systems under T-Mixing
5.4 Thermal Relaxation to Equilibrium: The Canonical Ensemble
5.5 Relaxation to Quasi-Equilibrium for Nonergodic Systems
5.6 Aside: The Thermodynamic Connection
5.7 Introduction to Classical Thermodynamics
5.A Appendix: Entropy Change for a Cyclic Temperature Variation
 

6 NONEQUILIBRIUM STEADY STATES
6.1 The Physically Ergodic Nonequilibrium Steady State
6.2 Dissipation in Nonequilibrium Steady States (NESSs)
6.3 For T-Mixing Systems, Nonequilibrium Steady-State Averages are Independent of the Initial Equilibrium Distribution
6.4 In the Linear Response Steady State, the Dissipation is Minimal with
Respect to Variations of the Initial Distribution
6.5 Sum Rules for

Denis J. Evans is professor of physics in the Department of Applied Mathematics, Research School of Physics and Engineering, ANU, Canberra, Australia. Having obtained his Ph.D. from ANU, he worked at Oxford and Cornell Universities and the NIST Boulder CO before taking
up his present appointment. Professor Evans has authored ~300 scientific publications and two research monographs. He has received numerous scientific awards, including the Boys-Rahman Lectureship of the Royal Society of Chemistry (London), and the David Craig medal
of the Australian Academy of Sciences. He is also a Fellow of the Australian Academy of Sciences.
 
Debra J. Searles received her PhD in Chemistry from the University of Newcastle, Australia. She held postdoctoral research positions at University of Basel, Switzerland, The Australian National University and University of Queensland, Australia. She joined Griffith University in 2000, becoming professor in 2009 and moved to the University of Queensland in 2012 where she has appointments in the Australian Institute for Bioengineering and Nanotechnology and the School of Chemistry and Molecular Biosciences. Since 2013 she has been Director of
the AIBN Centre for Theoretical and Computational Molecular Science. She has 140 publications and is a Fellow of the Royal Australian Chemical Institute.
 
Stephen R. Williams received his PhD in Physics from RMIT University in Melbourne. He was a postdoc at Utrecht University and has been at the Australian National University since 2003 where he is currently a Senior Research Fellow.