close
1.

図書

図書
Josef Honerkamp
出版情報: Berlin : Springer, c2002  xiv, 515 p. ; 24 cm
シリーズ名: Advanced texts in physics
所蔵情報: loading…
目次情報: 続きを見る
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:
2.

図書

図書
edited by J. Honerkamp, K. Pohlmeyer and H. Römer
出版情報: New York : Plenum Press, c1983  ix, 378 p. ; 26 cm
シリーズ名: NATO advanced study institutes series ; ser. B . Physics ; v. 82
所蔵情報: loading…
3.

図書

図書
Josef Honerkamp ; translated by Katja Lindenberg
出版情報: New York : VCH, c1994  xvi, 535 p. ; 25 cm
所蔵情報: loading…
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼