Statistical Mechanics: Entropy, Order Parameters, and Complexity

Description

A new and updated edition of the successful Statistical Mechanics: Entropy, Order Parameters and Complexity from 2006. Statistical mechanics is a core topic in modern physics. Innovative, fresh introduction to the broad range of topics of statistical mechanics today, by brilliant teacher and renowned researcher.

• Broad perspective on statistical mechanics as tool for deriving new laws.
• 80 in-depth exercises in astrophysics, computer science, biology, and social sciences.
• Avoids traditional focus on molecules, thermodynamics, and quantum mechanics.
• 70 in-class activities, 33 exercises to test comprehension.
• 50 ambitious computational exercises, with hint notebooks in Mathematica and Python.

New to this edition

• The number of exercises is almost doubled, with wide-ranging applications to many fields of science.
• New exercises designed for 'flipped classroom' and remote instruction; handouts and instructions for in-class activities.
• 50 ambitious computational exercises, accompanied by hint notebooks in Python and Mathematica.
• Polished answer key available for instructors, with additional teaching content for many exercises.

About the Author(s)

James P. Sethna, Professor of Physics, Cornell University

James P. Sethna is professor of physics at Cornell University. Sethna has used statistical mechanics to make substantive contributions in a bewildering variety of subjects — mathematics (dynamical systems and the onset of chaos), engineering (microstructure, plasticity, and fracture), statistics (information geometry, sloppy models, low-dimensional embeddings), materials science (glasses and spin glasses, liquid crystals, crackling noise, superconductivity), and popular culture (mosh pit dynamics and zombie outbreak epidemiology). He has collected cool, illustrative problems from students and colleagues over the decades, which inspired this textbook.

Table of Contents

Preface
Contents
List of figures
What is statistical mechanics?
1.1:Quantum dice and coins
1.2:Probability distributions
1.3:Waiting time paradox
1.4:Stirling’s formula
1.5:Stirling and asymptotic series
1.6:Random matrix theory
1.7:Six degrees of separation
1.8:Satisfactory map colorings
1.9:First to fail: Weibull
1.10:Emergence
1.11:Emergent vs. fundamental
1.12:Self-propelled particles
1.13:The birthday problem
1.14:Width of the height distribution
1.15:Fisher information and Cram´er–Rao
1.16:Distances in probability space
Random walks and emergent properties
2.1:Random walk examples: universality and scale invariance
2.2:The diffusion equation
2.3:Currents and external forces
2.4:Solving the diffusion equation
Temperature and equilibrium
3.1:The microcanonical ensemble
3.2:The microcanonical ideal gas
3.3:What is temperature?
3.4:Pressure and chemical potential
3.5:Entropy, the ideal gas, and phase-space refinements
Phase-space dynamics and ergodicity
4.1:Liouville’s theorem
4.2:Ergodicity
Entropy
5.1:Entropy as irreversibility: engines and the heat death of the Universe
5.2:Entropy as disorder
5.3:Entropy as ignorance: information and memory
Free energies
6.1:The canonical ensemble
6.2:Uncoupled systems and canonical ensembles
6.3:Grand canonical ensemble
6.4:What is thermodynamics?
6.5:Mechanics: friction and fluctuations
6.6:Chemical equilibrium and reaction rates
6.7:Free energy density for the ideal gas
Quantum statistical mechanics
7.1:Mixed states and density matrices
7.2:Quantum harmonic oscillator
7.3:Bose and Fermi statistics
7.4:Non-interacting bosons and fermions
7.5:Maxwell–Boltzmann ‘quantum’ statistics
7.6:Black-body radiation and Bose condensation
7.7:Metals and the Fermi gas
Calculation and computation
8.1:The Ising model
8.2:Markov chains
8.3:What is a phase? Perturbation theory
Order parameters, broken symmetry, and topology
9.1:Identify the broken symmetry
9.2:Define the order parameter
9.3:Examine the elementary excitations
9.4:Classify the topological defects
Correlations, response, and dissipation
10.1:Correlation functions: motivation
10.2:Experimental probes of correlations
10.3:Equal-time correlations in the ideal gas
10.4:Onsager’s regression hypothesis and time correlations
10.5:Susceptibility and linear response
10.6:Dissipation and the imaginary part
10.7:Static susceptibility
10.8:The fluctuation-dissipation theorem
10.9:Causality and Kramers–Kr¨onig
Abrupt phase transitions
11.1:Stable and metastable phases
11.2:Maxwell construction
11.3:Nucleation: critical droplet theory
11.4:Morphology of abrupt transitions
Continuous phase transitions
12.1:Universality
12.2:Scale invariance
12.3:Examples of critical points
A Appendix: Fourier methods
A.1:Fourier conventions
A.2:Derivatives, convolutions, and correlations
A.3:Fourier methods and function space
A.4:Fourier and translational symmetry
References
Index

Reviews

"Review from previous edition Since the book treats intersections of mathematics, biology, engineering, computer science and social sciences, it will be of great help to researchers in these fields in making statistical mechanics useful and comprehensible. At the same time, the book will enrich the subject for physicists who'd like to apply their skills in other disciplines. [...] The author's style, although quite concentrated, is simple to understand, and has many lovely visual examples to accompany formal ideas and concepts, which makes the exposition live and intuitvely appealing." - Olga K. Dudko, Journal of Statistical Physics, Vol 126

"Sethna's book provides an important service to students who want to learn modern statistical mechanics. The text teaches students how to work out problems by guiding them through the exercises rather than by presenting them with worked-out examples. " - Susan Coppersmith, Physics Today, May 2007