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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
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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 Massimo Picardello, Wolfgang Woess
出版情報: Cambridge : Cambridge University Press, 1999  viii, 361 p. ; 24 cm
シリーズ名: Symposia mathematica ; v. 39
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3.

図書

図書
Walter E. Thirring ; with foreword by Elliott H. Lieb
出版情報: Providence, R.I. : American Mathematical Society, c1998  xiii, 729 p. ; 26 cm
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4.

図書

図書
R.A. Minlos
出版情報: Providence, RI : American Mathematical Society, c2000  vii, 103 p. ; 26 cm
シリーズ名: University lecture series ; v. 19
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5.

図書

図書
Nandita Rudra, P. Rudra
出版情報: Hackensack : World Scientific, c2010  xvii, 229 p. ; 24 cm
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目次情報: 続きを見る
Preface
Notations and Fundamental Constants
Basic Concepts / 1:
Introduction / 1.1:
Master Equation and Hypothesis of Equal á-priori Probability / 1.2:
Example of 3 Level Systems / 1.2.1:
Phase Space, Phase Point, Phase Trajectory / 1.3:
Statistical Distribution Function and Ergodic Hypothesis / 1.4:
Statistical Fluctuation and Statistical Independence / 1.5:
Statistical Fluctuation and Generalized Susceptibility / 1.6:
Generalized Ornstein-Zernicke Relation / 1.7:
Problems / 1.8:
Motion of Systems in Phase Space / 2:
Integral Invariants / 2.1:
Classical Liouville's Equation / 2.2:
Role of Energy / 2.3:
Quantum Mechanical Density Matrix / 2.4:
Quantum Liouville's Equation / 2.5:
States in Statistical Physics / 2.6:
Microscopic and Macroscopic States / 3.1:
Statistical Weight and Density of States / 3.2:
Examples: Non-interacting One- and N-Particle Systems and Spin-1/2 Particles / 3.3:
Entropy and Boltzmann's Principle / 3.4:
Boltzmann's H-Theorem / 3.5:
Statistical Ensembles / 3.6:
Microcanonical Distribution Function / 4.1:
Canonical (Gibbs) Distribution Function / 4.3:
Thermodynamic Temperature and Distribution Function / 4.3.1:
Spin-1/2 Particles and Negative Temperature / 4.3.2:
Partition Function and Different Thermodynamic Functions / 4.3.3:
System of Linear Harmonic Oscillators in Canonical Ensemble / 4.3.4:
Energy Fluctuation in Canonical Ensemble and Equivalence of Canonical and Microcanonical Ensembles / 4.3.5:
Grandcanonical Distribution Function / 4.4:
Dependence of Thermodynamic Functions on Number of Particles / 4.4.1:
Chemical Potential and Distribution Function / 4.4.2:
Density Fluctuation in Grandcanonical Ensemble and Equivalence of Grandcanonical and Canonical Ensembles / 4.4.3:
Ideal Gas / 4.5:
Boltzmann Distribution / 5.1:
Partition Function, Free Energy and Equation of State / 5.2:
Specific Heat: Translational, Vibrational and Rotational Components / 5.3:
Degeneracy Temperature / 5.4:
Chemical Reaction Equilibrium / 5.5:
Conditions of Chemical Equilibrum / 6.1:
Law of Mass Action / 6.2:
Heat of Reaction and Direction of Reaction / 6.3:
Ionization Equilibrium / 6.4:
Saha Formula / 6.5:
Real Gas / 6.6:
Free Energy, Virial Equation of State / 7.1:
Second Virial Coefficient and Applicability of Virial Equation / 7.2:
Model Calculation and van-der-Waal's Equation of State / 7.3:
Joule-Thomson Expansion and Inversion Temperature / 7.4:
Strong Electrolytes / 7.5:
Debye-Hückel Approximation, Debye Length / 8.1:
Screened Coulomb Potential / 8.2:
Equation of State and Osmotic Pressure / 8.3:
Quantum Statistics / 8.4:
Bose and Fermi Distributions / 9.1:
Quantum Gases of Elementary Particles: Number Density and Chemical Potential, Energy Density, Equation of State / 9.2:
Black Body Radiation and Planck's Law / 9.3:
Lattice Specific Heat and Phonons / 9.4:
Degenerate Bose Gas, Bose Condensation / 9.5:
Liquid He and Superfluidity / 9.6:
Systematics of Liquid 4He / 9.6.1:
Landau's 2-Fluid Model / 9.6.2:
Systematics of Liquid 3He / 9.6.3:
Degenerate Fermi Gas, Degeneracy Pressure, Specific Heat / 9.7:
Magnetism of Free Fermions / 9.8:
Preamble / 9.8.1:
Landau Diamagnetism / 9.8.2:
Pauli Paramagnetism / 9.8.3:
Interacting Fermi System: Fermi Liquid Theory / 9.9:
Relativistic Degenerate Fermi Gas / 9.10:
Bose-Einstein Condensate / 9.11:
Trapping of Atoms / 10.1:
Cooling of Atoms / 10.3:
Statistical Astrophysics / 10.4:
Stars: Stability and Evolution / 11.1:
High Temperature Dense Matter / 11.3:
Neutron Stars and Black Holes / 11.4:
Phase Transitions / 11.5:
Systematics of Phase Transitions / 12.1:
Ehrenfest's Classification of Phase Transitions / 12.2:
Order Parameter, Continuous and Discontinuous Transitions / 12.3:
Landau's Theory of Continuous Phase Transitions / 12.4:
Continuity of Entropy and Discontinuity of Specific Heat / 12.5:
Generalized Susceptibility / 12.6:
Critical Exponents and Fluctuations of Order Parameter / 12.7:
Ising Model / 12.8:
Zero-Field 1-Dimensional Case / 12.8.1:
Non-Zero-Field 1-Dimensional Case / 12.8.2:
Multi-Dimensional Case / 12.8.3:
2-Dimensional Ising System / 12.8.4:
Irreversible Processes / 12.9:
Linear Response Theory (Kubo Formalism) / 13.1:
Mechanical Process / 13.2.1:
Thermal Process / 13.2.2:
Symmetry Relations / 13.3:
Fluctuation-Dissipation Theorem / 13.4:
Mathematical Appendix / 13.5:
Beta and Gamma Functions / 14.1:
Dirac Delta Function (Distribution) / 14.2:
Functional Derivative / 14.3:
Mathematical Identities / 14.4:
Multiple Summation / 14.5:
Pauli Matrices / 14.6:
Probability Theory / 14.7:
Elementary Results of Probability Theory / 14.7.1:
Statistical Distributions / 14.7.2:
Central Limit Theorem / 14.7.3:
Quantum Mechanics, A Retrospect / 14.8:
Riemann, Bernoulli and Fourier / 14.9:
Riemann's ζ-Function / 14.9.1:
Bernoulli Numbers and Polynomials / 14.9.2:
Fourier Series / 14.9.3:
Integrals of Quantum Statistics / 14.9.4:
Sanskrit Transliteration / 14.10:
Stirling's Theorem / 14.11:
Summation and Integration / 14.12:
Volume of an N-Dimensional Sphere / 14.13:
Bibliography
Index
Preface
Notations and Fundamental Constants
Basic Concepts / 1:
6.

図書

図書
A.I. Akhiezer and S.V. Peletminskii ; translated by M. Schukin
出版情報: Oxford ; New York : Pergamon Press, c1981  xv, 450 p. ; 23 cm
シリーズ名: International series in natural philosophy ; v. 104
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7.

図書

図書
by E.M. Lifshitz and L.P. Pitaevskiĭ ; translated from the Russian by J.B. Sykes and M.J. Kearsley
出版情報: Oxford : Butterworth-Heinemann, 1995, c1980  x, 387 p. ; 25 cm
シリーズ名: Course of theoretical physics ; v. 9 . Statistical physics / L.D. Landau and E. M. Lifshitz ; pt. 2
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Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
Solids
Non-ideal gases
Solutions
Chemical reactions
Fluctuations
Surfaces
Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
8.

図書

図書
edited by Elizabeth Garber, Stephen G. Brush, and C.W.F. Everitt
出版情報: Cambridge, Mass. : MIT Press, c1986  xxvii, 565 p. ; 24 cm
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9.

図書

図書
出版情報: Malabar, Fla. : R.E. Krieger, 1986  xx, 520 p. ; 28 cm
シリーズ名: Statistical and thermal physics / by Shigeji Fujita ; pt. 1
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10.

図書

図書
by Yu.L. Klimontovich ; translated from the Russian by G. Pontecorvo
出版情報: Chur, Switzerland ; New York : Harwood Academic Publishers, c1986  xxvi, 734 p. ; 24 cm
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