Statistical physics : an advanced approach with applications : web-enhanced with problems and solutions

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Statistical physics : an advanced approach with applications : web-enhanced with problems and solutions / Josef Honerkamp

版:: 2nd ed.
資料種別:: 図書
出版情報:: Berlin : Springer, c2002
形態:: xiv, 515 p. ; 24 cm
シリーズ名:: Advanced texts in physics <BA44414285>
著者名:: Honerkamp, J. <DA03738555>
ISBN:: 9783540430209 [3540430202]
書誌ID:: BA56612333

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注記:

Includes bibliographical references (p. [503]-508) and index
With 109 figures, 7 tables and 57 problems with solutions

主題:

Statistical physics

言語:

英語

目次情報:

Statistical Physics Is More than Statistical Mechanics / 1：

Modeling of Statistical Systems / Part I：

Random Variables: Fundamentals of Probability Theory and Statistics / 2：

Probability and Random Variables / 2.1：

The Space of Events / 2.1.1：

Introduction of Probability / 2.1.2：

Random Variables / 2.1.3：

Multivariate Random Variables and Conditional Probabilities / 2.2：

Multidimensional Random Variables / 2.2.1：

Marginal Densities / 2.2.2：

Conditional Probabilities and Bayes' Theorem / 2.2.3：

Moments and Quantiles / 2.3：

Moments / 2.3.1：

Quantiles / 2.3.2：

The Entropy / 2.4：

Entropy for a Discrete Set of Events / 2.4.1：

Entropy for a Continuous Space of Events / 2.4.2：

Relative Entropy / 2.4.3：

Remarks / 2.4.4：

Applications / 2.4.5：

Computations with Random Variables / 2.5：

Addition and Multiplication of Random Variables / 2.5.1：

Further Important Random Variables / 2.5.2：

Limit Theorems / 2.5.3：

Stable Random Variables and Renormalization Transformations / 2.6：

Stable Random Variables / 2.6.1：

The Renormalization Transformation / 2.6.2：

Stability Analysis / 2.6.3：

Scaling Behavior / 2.6.4：

The Large Deviation Property for Sums of Random Variables / 2.7：

Random Variables in State Space: Classical Statistical Mechanics of Fluids / 3：

The Microcanonical System / 3.1：

Systems in Contact / 3.2：

Thermal Contact / 3.2.1：

Systems with Exchange of Volume and Energy / 3.2.2：

Systems with Exchange of Particles and Energy / 3.2.3：

Thermodynamic Potentials / 3.3：

Susceptibilities / 3.4：

Heat Capacities / 3.4.1：

Isothermal Compressibility / 3.4.2：

Isobaric Expansivity / 3.4.3：

Isochoric Tension Coefficient and Adiabatic Compressibility / 3.4.4：

A General Relation Between Response Functions / 3.4.5：

The Equipartition Theorem / 3.5：

The Radial Distribution Function / 3.6：

Approximation Methods / 3.7：

The Virial Expansion / 3.7.1：

Integral Equations for the Radial Distribution Function / 3.7.2：

Perturbation Theory / 3.7.3：

The van der Waals Equation / 3.8：

The Isotherms / 3.8.1：

The Maxwell Construction / 3.8.2：

Corresponding States / 3.8.3：

Critical Exponents / 3.8.4：

Some General Remarks about Phase Transitions and Phase Diagrams / 3.9：

Random Fields: Textures and Classical Statistical Mechanics of Spin Systems / 4：

Discrete Stochastic Fields / 4.1：

Markov Fields / 4.1.1：

Gibbs Fields / 4.1.2：

Equivalence of Gibbs and Markov Fields / 4.1.3：

Examples of Markov Random Fields / 4.2：

Model with Independent Random Variables / 4.2.1：

Auto Model / 4.2.2：

Multilevel Logistic Model / 4.2.3：

Gauss Model / 4.2.4：

Characteristic Quantities of Densities for Random Fields / 4.3：

Simple Random Fields / 4.4：

The White Random Field or the Ideal Paramagnetic System / 4.4.1：

The One-Dimensional Ising Model / 4.4.2：

Random Fields with Phase Transitions / 4.5：

The Curie-Weiss Model / 4.5.1：

The Mean Field Approximation / 4.5.2：

The Two-Dimensional Ising Model / 4.5.3：

The Landau Free Energy / 4.6：

The Renormalization Group Method for Random Fields and Scaling Laws / 4.7：

Scaling Laws / 4.7.1：

Time-Dependent Random Variables: Classical Stochastic Processes / 5：

Markov Processes / 5.1：

The Master Equation / 5.2：

Examples of Master Equations / 5.3：

Analytic Solutions of Master Equations / 5.4：

Equations for the Moments / 5.4.1：

The Equation for the Characteristic Function / 5.4.2：

Examples / 5.4.3：

Simulation of Stochastic Processes and Fields / 5.5：

The Fokker-Planck Equation / 5.6：

Fokker-Planck Equation with Linear Drift Term and Additive Noise / 5.6.1：

The Linear Response Function and the Fluctuation-Dissipation Theorem / 5.7：

The [Omega] Expansion / 5.8：

The One-Particle Picture / 5.8.2：

More General Stochastic Processes / 5.9：

Self-Similar Processes / 5.9.1：

Fractal Brownian Motion / 5.9.2：

Stable Levy Processes / 5.9.3：

Autoregressive Processes / 5.9.4：

Quantum Random Systems / 6：

Quantum-Mechanical Description of Statistical Systems / 6.1：

Ideal Quantum Systems: General Considerations / 6.2：

Expansion in the Classical Regime / 6.2.1：

First Quantum-Mechanical Correction Term / 6.2.2：

Relations Between the Thermodynamic Potential and Other System Variables / 6.2.3：

The Ideal Fermi Gas / 6.3：

The Fermi-Dirac Distribution / 6.3.1：

Determination of the System Variables at Low Temperatures / 6.3.2：

Applications of the Fermi-Dirac Distribution / 6.3.3：

The Ideal Bose Gas / 6.4：

Particle Number and the Bose-Einstein Distribution / 6.4.1：

Bose-Einstein Condensation / 6.4.2：

Pressure / 6.4.3：

Energy and Specific Heat / 6.4.4：

Entropy / 6.4.5：

Applications of Bose Statistics / 6.4.6：

The Photon Gas and Black Body Radiation / 6.5：

The Kirchhoff Law / 6.5.1：

The Stefan-Boltzmann Law / 6.5.2：

The Pressure of Light / 6.5.3：

The Total Radiative Power of the Sun / 6.5.4：

The Cosmic Background Radiation / 6.5.5：

Lattice Vibrations in Solids: The Phonon Gas / 6.6：

Systems with Internal Degrees of Freedom: Ideal Gases of Molecules / 6.7：

Magnetic Properties of Fermi Systems / 6.8：

Diamagnetism / 6.8.1：

Paramagnetism / 6.8.2：

Quasi-particles / 6.9：

Models for the Magnetic Properties of Solids / 6.9.1：

Superfluidity / 6.9.2：

Changes of External Conditions / 7：

Reversible State Transformations, Heat, and Work / 7.1：

Cyclic Processes / 7.2：

Exergy and Relative Entropy / 7.3：

Time Dependence of Statistical Systems / 7.4：

Analysis of Statistical Systems / Part II：

Estimation of Parameters / 8：

Samples and Estimators / 8.1：

Confidence Intervals / 8.2：

Propagation of Errors / 8.3：

The Maximum Likelihood Estimator / 8.4：

The Least-Squares Estimator / 8.5：

Signal Analysis: Estimation of Spectra / 9：

The Discrete Fourier Transform and the Periodogram / 9.1：

Filters / 9.2：

Filters and Transfer Functions / 9.2.1：

Filter Design / 9.2.2：

Consistent Estimation of Spectra / 9.3：

Frequency Distributions for Nonstationary Time Series / 9.4：

Filter Banks and Discrete Wavelet Transformations / 9.5：

Wavelets / 9.6：

Wavelets as Base Functions in Function Spaces / 9.6.1：

Wavelets and Filter Banks / 9.6.2：

Solutions of the Dilation Equation / 9.6.3：

Estimators Based on a Probability Distribution for the Parameters / 10：

Bayesian Estimator and Maximum a Posteriori Estimator / 10.1：

Marginalization of Nuisance Parameters / 10.2：

Numerical Methods for Bayesian Estimators / 10.3：

Identification of Stochastic Models from Observations / 11：

Hidden Systems / 11.1：

The Maximum a Posteriori (MAP) Estimator for the Inverse Problem / 11.2：

The Least-Squares Estimator as a Special MAP Estimator / 11.2.1：

Strategies for Choosing the Regularization Parameter / 11.2.2：

The Regularization Method / 11.2.3：

Examples of Estimating a Distribution Function by a Regularization Method / 11.2.4：

Estimating the Realization of a Hidden Process / 11.3：

The Viterbi Algorithm / 11.3.1：

The Kalman Filter / 11.3.2：

Estimating the Parameters of a Hidden Stochastic Model / 12：

The Expectation Maximization Method (EM Method) / 12.1：

Use of the EM Method for Estimation of the Parameters in Hidden Systems / 12.2：

Estimating the Parameters of a Hidden Markov Model / 12.3：

The Forward Algorithm / 12.3.1：

The Backward Algorithm / 12.3.2：

The Estimation Formulas / 12.3.3：

Estimating the Parameters in a State Space Model / 12.4：

Statistical Tests and Classification Methods / 13：

General Comments Concerning Statistical Tests / 13.1：

Test Quantity and Significance Level / 13.1.1：

Empirical Moments for a Test Quantity: The Bootstrap Method / 13.1.2：

The Power of a Test / 13.1.3：

Some Useful Tests / 13.2：

The z- and the t-Test / 13.2.1：

Test for the Equality of the Variances of Two Sets of Measurements, the F-Test / 13.2.2：

The x[superscript 2]-Test / 13.2.3：

The Kolmogorov-Smirnov Test / 13.2.4：

The F-Test for Least-Squares Estimators / 13.2.5：

The Likelihood-Ratio Test / 13.2.6：

Classification Methods / 13.3：

Classifiers / 13.3.1：

Estimation of Parameters That Arise in Classifiers / 13.3.2：

Automatic Classification (Cluster Analysis) / 13.3.3：

Random Number Generation for Simulating Realizations of Random Variables / Appendix：

Problems

Hints and Solutions

References

Index

Statistical Physics Is More than Statistical Mechanics / 1：

Modeling of Statistical Systems / Part I：

Random Variables: Fundamentals of Probability Theory and Statistics / 2：

Probability and Random Variables / 2.1：

The Space of Events / 2.1.1：

Introduction of Probability / 2.1.2：

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