Introduction to Statistical Physics

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Written by a world-renowned theoretical physicist, Introduction to Statistical Physics, Second Edition clarifies the properties of matter collectively in terms of the physical laws governing atomic motion. This second edition expands upon the original to include many additional exercises and more pedagogically oriented discussions that fully explain the concepts and applications. The book first covers the classical ensembles of statistical mechanics and stochastic processes, including Brownian motion, probability theory, and the Fokker--Planck and Langevin equations. To illustrate the use of statistical methods beyond the theory of matter, the author discusses entropy in information theory, Brownian motion in the stock market, and the Monte Carlo method in computer simulations. The next several chapters emphasize the difference between quantum mechanics and classical mechanics--the quantum phase. Applications covered include Fermi statistics and semiconductors and Bose statistics and Bose--Einstein condensation. The book concludes with advanced topics, focusing on the Ginsburg--Landau theory of the order parameter and the special kind of quantum order found in superfluidity and superconductivity. Assuming some background knowledge of classical and quantum physics, this textbook thoroughly familiarizes advanced undergraduate students with the different aspects of statistical physics. This updated edition continues to provide the tools needed to understand and work with random processes.

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A Macroscopic View of Matter Viewing the World at Different Scales Thermodynamics The Thermodynamic Limit Thermodynamic Transformations Classic Ideal Gas First Law of Thermodynamics Magnetic Systems Heat and Entropy The Heat Equations Applications to Ideal Gas Carnot Cycle Second Law of Thermodynamics Absolute Temperature Temperature as Integrating Factor Entropy Entropy of Ideal Gas The Limits of Thermodynamics Using Thermodynamics The Energy Equation Some Measurable Coefficients Entropy and Loss TS Diagram Condition for Equilibrium Helmholtz Free Energy Gibbs Potential Maxwell Relations Chemical Potential Phase Transitions First-Order Phase Transition Condition for Phase Coexistence Clapeyron Equation Van der Waals Equation of State Virial Expansion Critical Point Maxwell Construction Scaling Nucleation and Spinodal Decomposition The Statistical Approach The Atomic View Random Walk Phase Space Distribution Function Ergodic Hypothesis Statistical Ensemble Microcanonical Ensemble Correct Boltzmann Counting Distribution Entropy: Boltzmann's H The Most Probable Distribution Information Theory: Shannon Entropy Maxwell-Boltzmann Distribution Determining the Parameters Pressure of Ideal Gas Equipartition of Energy Distribution of Speed Entropy Derivation of Thermodynamics Fluctuations The Boltzmann Factor Time's Arrow Transport Phenomena Collisionless and Hydrodynamic Regimes Maxwell's Demon Nonviscous Hydrodynamics Sound Wave Diffusion Heat Conduction Viscosity Navier-Stokes Equation Canonical Ensemble Review of the Microcanonical Ensemble Classical Canonical Ensemble The Partition Function Connection with Thermodynamics Energy Fluctuations Minimization of Free Energy Classical Ideal Gas Grand Canonical Ensemble The Particle Reservoir Grand Partition Function Number Fluctuations Connection with Thermodynamics Parametric Equation of State and Virial Expansion Critical Fluctuations Pair Creation Noise Thermal Fluctuations Nyquist Noise Brownian Motion Einstein's Theory Diffusion Einstein's Relation Molecular Reality Fluctuation and Dissipation Brownian Motion of the Stock Market Stochastic Processes Randomness and Probability Binomial Distribution Poisson Distribution Gaussian Distribution Central Limit Theorem Shot Noise Time-Series Analysis Ensemble of Paths Ensemble Average Power Spectrum and Correlation Function Signal and Noise Transition Probabilities Markov Process Fokker-Planck Equation The Monte Carlo Method Simulation of the Ising Model The Langevin Equation The Equation and Solution Energy Balance Fluctuation-Dissipation Theorem Diffusion Coefficient and Einstein's Relation Transition Probability: Fokker-Planck Equation Heating by Stirring: Forced Oscillator in Medium Quantum Statistics Thermal Wavelength Identical Particles Occupation Numbers Spin Microcanonical Ensemble Fermi Statistics Bose Statistics Determining the Parameters Pressure Entropy Free Energy Equation of State Classical Limit Quantum Ensembles Incoherent Superposition of States Density Matrix Canonical Ensemble (Quantum-Mechanical) Grand Canonical Ensemble (Quantum-Mechanical) Occupation Number Fluctuations Photon Bunching The Fermi Gas Fermi Energy Ground State Fermi Temperature Low-Temperature Properties Particles and Holes Electrons in Solids Semiconductors The Bose Gas Photons Bose Enhancement Phonons Debye Specific Heat Electronic Specific Heat Conservation of Particle Number Bose-Einstein Condensation Macroscopic Occupation The Condensate Equation of State Specific Heat How a Phase Is Formed Liquid Helium The Order Parameter The Essence of Phase Transitions Ginsburg-Landau Theory Relation to Microscopic Theory Functional Integration and Differentiation Second-Order Phase Transition Mean-Field Theory Critical Exponents The Correlation Length First-Order Phase Transition Cahn-Hilliard Equation Superfluidity Condensate Wave Function Spontaneous Symmetry Breaking Mean-Field Theory Observation of Bose-Einstein Condensation Quantum Phase Coherence Superfluid Flow Phonons: Goldstone Mode Superconductivity Meissner Effect Magnetic Flux Quantum Josephson Junction DC Josephson Effect AC Josephson Effect Time-Dependent Vector Potential The SQUID Broken Symmetry Appendix Index Problems appear at the end of each chapter.

Kerson Huang is Professor of Physics, Emeritus at MIT. Since retiring from active teaching, Dr. Huang has been engaged in biophysics research.

! suitable for advanced engineering study in an engineering or physics curriculum. ! The problems at the end of each chapter and the discussion of applications will help students grasp many difficult concepts. ! very readable and should be considered for an undergraduate program or by people wanting to learn about statistical physics. --IEEE Electrical Insulation Magazine, Vol. 27, No. 3, May/June 2011

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