Statistical Mechanics: Entropy, Order Parameters, and Complexity
Second Edition
Series: Oxford Master Series in Physics; 14;
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Product details:
- Edition number 2
- Publisher OUP Oxford
- Date of Publication 26 January 2021
- ISBN 9780198865254
- Binding Paperback
- No. of pages492 pages
- Size 23x189x246 mm
- Weight 1012 g
- Language English
- Illustrations 230 line drawings 174
Categories
Short 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.
MoreLong description:
Statistical mechanics is our tool for deriving the laws that emerge from complex systems. Sethna's text distills the subject to be accessible to those in all realms of science and engineering -- avoiding extensive use of quantum mechanics, thermodynamics, and molecular physics. Statistical mechanics explains how bacteria search for food, and how DNA replication is proof-read in biology; optimizes data compression, and explains transitions in complexity in computer science; explains the onset of chaos, and launched random matrix theory in mathematics; addresses extreme events in engineering; and models pandemics and language usage in the social sciences. Sethna's exercises introduce physicists to these triumphs and a hundred others -- broadening the horizons of scholars both practicing and nascent. Flipped classrooms and remote learning can now rely on 33 pre-class exercises that test reading comprehension (Emergent vs. fundamental; Weirdness in high dimensions; Aging, entropy and DNA), and 70 in-class activities that illuminate and broaden knowledge (Card shuffling; Human correlations; Crackling noises). Science is awash in information, providing ready access to definitions, explanations, and pedagogy. Sethna's text focuses on the tools we use to create new laws, and on the fascinating simple behavior in complex systems that statistical mechanics explains.
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.
Table of Contents:
Preface
Contents
List of figures
What is statistical mechanics?
Quantum dice and coins
Probability distributions
Waiting time paradox
Stirling?s formula
Stirling and asymptotic series
Random matrix theory
Six degrees of separation
Satisfactory map colorings
First to fail: Weibull
Emergence
Emergent vs. fundamental
Self-propelled particles
The birthday problem
Width of the height distribution
Fisher information and Cram´er?Rao
Distances in probability space
Random walks and emergent properties
Random walk examples: universality and scale invariance
The diffusion equation
Currents and external forces
Solving the diffusion equation
Temperature and equilibrium
The microcanonical ensemble
The microcanonical ideal gas
What is temperature?
Pressure and chemical potential
Entropy, the ideal gas, and phase-space refinements
Phase-space dynamics and ergodicity
Liouville?s theorem
Ergodicity
Entropy
Entropy as irreversibility: engines and the heat death of the Universe
Entropy as disorder
Entropy as ignorance: information and memory
Free energies
The canonical ensemble
Uncoupled systems and canonical ensembles
Grand canonical ensemble
What is thermodynamics?
Mechanics: friction and fluctuations
Chemical equilibrium and reaction rates
Free energy density for the ideal gas
Quantum statistical mechanics
Mixed states and density matrices
Quantum harmonic oscillator
Bose and Fermi statistics
Non-interacting bosons and fermions
Maxwell?Boltzmann ?quantum? statistics
Black-body radiation and Bose condensation
Metals and the Fermi gas
Calculation and computation
The Ising model
Markov chains
What is a phase? Perturbation theory
Order parameters, broken symmetry, and topology
Identify the broken symmetry
Define the order parameter
Examine the elementary excitations
Classify the topological defects
Correlations, response, and dissipation
Correlation functions: motivation
Experimental probes of correlations
Equal-time correlations in the ideal gas
Onsager?s regression hypothesis and time correlations
Susceptibility and linear response
Dissipation and the imaginary part
Static susceptibility
The fluctuation-dissipation theorem
Causality and Kramers?Kr¨onig
Abrupt phase transitions
Stable and metastable phases
Maxwell construction
Nucleation: critical droplet theory
Morphology of abrupt transitions
Continuous phase transitions
Universality
Scale invariance
Examples of critical points
A Appendix: Fourier methods
Fourier conventions
Derivatives, convolutions, and correlations
Fourier methods and function space
Fourier and translational symmetry
References
Index
