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Statistical Mechanics |
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R. C. Tolman, The Principles of Statistical Mechanics (Oxford, 1938). | |
R. C. Tolman, Statistical Mechanics with Applications to Physics and Chemistry (Chemical Catalog Company, 1927). | |
J. E. and M. G. Mayer, Statistical Mechanics (Wiley, 1940). | |
R. B. Lindsay, Introduction to Physical Statistics (Wiley, 1941). | |
L. D. Landau and E. M. Lifschitz, Statistical Physics (Oxford, 1938). | |
P. and T. Ehrenfest, The Conceptual Foundations of the Statistical Approach to Mechanics (Dover, 1990). | |
P. Caldirola, Riv. Nuovo Cimento 2, 25 (1946). | |
K. F. Herzfeld, "Kinetische Theorie der Wärme," Müller-Pouillets Lehrbuch der Physik, Band 3 (Vieweg, 1925). | |
M. A. Leontovich, Statisticheskaya Fizika (Gostekhizdat, 1944). | |
R. W. Gurney, Introduction to Statistical Mechanics (McGraw-Hill, 1949). | |
G. S. Rushbrooke, Introduction to Statistical Mechanics (Oxford, 1949). | |
R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics (Cambridge, 1939). | |
A. Haas, ed, Commentary on the Scientific Writings of J. Willard Gibbs," (Yale, 1936). | |
R. B. Lindsay and H. Margenau, Foundations of Physics (Wiley, 1936). | |
I. Fraquhar, Ergodic Theory in Statistical Mechanics (Wiley, 1965). | |
G. Wannier, Statistical Physics," (Wiley, 1966). | |
T. A. Bak, ed., Statistical Mechanics: Foundations and Applications (Benjamin, 1965). | |
A. Münster, Statistical Theromodynamics (Springer, 1956). | |
D. Ter Haar, Foundations of Statistical Mechanics Rev. Mod. Phys. 27, 289 (1955). | |
C. Truesdell and D. Morgenstern, Ergebnisse der exakten Naturwiss. 30, 286 (1958). | |
N. N. Bogoliubov, The Problem of Dynamical Theory in Statistical Physics (Gostekhizdat, 1946). | |
R. C. Tolman, The Principles of Statistical Mechanics (Oxford, 1938). | |
J. De Boer and G. Uhlenbeck, Studies in Statistical Mechanics (North Holland, 1938). | |
D. Ruelle, Statistical Mechanics: Rigorious Results (Benjamin, 1969). | |
J. L. Lebowitz, Ann. Rev. Phys. Chem 19, 389 (1968). | |
J. E. Mayer, Equilibrium Statistical Mechanics (Oxford, 1968). | |
R. H. Furth, Fundamental Principles of Modern Theoretical Physics (Pergamon, 1970). | |
A. Münster, Statistical Theromodynamics (Springer, 1969). | |
E. G. D. Cohen, ed., Statistical Mechanics at the Turn of the Decade, (Marcel Dekker, 1971). | |
E. G. D. Cohen, Fundamental Problems in Statistical Mechanics, (North Holland, 1980). | |
A. Isihara, Statistical Physics (Academic Press, 1971). | |
C. J. Thompson, Mathematical Statistical Mechanics (MacMillan, 1972). | |
F. Mandl, Statistical Physics (Wiley, 1971). | |
J. Ehlers, Lecture Notes in Physics (Springer, 2002). | |
R. P. Feynman, Statistical Mechanics (Benjamin, 1972). | |
B. J. McClelland, Statistical Theromodynamics (Chapman and Hall, 1973). | |
K. Binder, ed., Monte Carlo Methods in Statistical Physics (Springer, 1979). | |
Y. B. Rumer and M. S. Ryvkin, Thermodynamics, Statistical Physics and Kinetics (Mir, 1980). | |
C. Kittel and H. Kroemer, Thermal Physics (W. H. Freeman, 1983). | |
M. Rasetti, Modern Methods in Equilibrium Statistical Mechanics (World, 1984). | |
S.-K. Ma, Statistical Mechanics (World, 1984). | |
K. Binder, ed., Applications of the Monte Carlo Method in Statistical Physics (Springer, 1984). | |
J. Fritz, A. Jaffe and D. Scasz, eds., Statistical Physics of Dynamical Systems: Rigorious Results (Birkhauser, 1985). | |
D. G. Chandler, Introduction to Modern Statistical Thermodynamics (Oxford, 1987). | |
B. H. Lavenda, Statistical Physics: A Probabilistic Approach (Wiley, 1992). | |
Foundations of Classical Statistics |
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R. C. Tolman, "On the Establishment of Grand Canonical Distributions," Phys. Rev. 57, 1160 (1940). | |
G. D. Birkhoff, "Proof of the Ergodic Theorem," Proc. Natl. Acad. Sci. 17, 656 (1931). | |
J. von Neumann, "Proof of the Quasi-Ergodic Hypothesis," Proc. Natl. Acad. Sci. 18, 70 (1932). | |
J. von Neumann, "Physical Applications of the Ergodic Hypothesis," Proc. Natl. Acad. Sci. 18, 263 (1932). | |
G. D. Birkhoff and B. O. Koopman, "Recent Contributions to the Ergodic Theory," Proc. Natl. Acad. Sci. 18, 279 (1932). | |
B. O. Koopman, "Hamiltonian Systems and Transformations in Hilbert Space," Proc. Natl. Acad. Sci. 17, 315 (1931). | |
E. Hopf, Ergodentheorie (Chelsea, 1948). | |
A. I. Kinchin, Mathematical Foundations of Statistical Mechanics (Dover, 1949). | |
L. Rosenfeld, Acta. Phys. Tol. 14, 3 (1955). | |
D. Bohm and W. Schëtzer, "The General Statistical Problem in Physics and the Theory of Probability," Nuovo Cimento, Suppl. 2, 1004 (1955). | |
T. Yamamoto and H. Matsuda, Prog. Theor. Phys. 16, 269 (1956). | |
L. Szilard, Z. Phys. 32, 753 (1925). | |
C. Mandelbrot, Comptes Rendus 243, 1835 (1956). | |
S. Albertoni, P. Bocchieri and A. Loinger, "New Theorem in the Classical Ensemble Theory," J. Math. Phys. 1, 244 (1960). | |
P. Bocchieri and A. Loinger, "Remarks on a Theorem in Classical Ensemble Theory," Phys. Lett. 4, 188 (1963). | |
L. Tisza and P. M. Quay, Ann. Phys. (N.Y.) 25, 48 (1963). | |
M. E. Fisher, Arch. Rat. Mech. Anal. 17, 377 (1964). | |
D. Ruelle, Helv. Phys. Acta 36, 183 (1963). | |
V. I. Arnol'd, "Small Denominators and Problems of Stability in Classical and Celestial Mechanics," Usp. Mat. Nauk 18, 91 (1963) [Russian Math. Surveys 18, 85 (1963)]. | |
D. V. Anosov and Y. G. Sinai, "Certain Smooth Ergodic Systems," Usp. Mat. Nauk 22, 107 (1967) [Russian Math. Surveys 22, 103 (1967)]. | |
J. L. Lebowitz and E. Lieb, "Existence of Thermodynamics for Real Matter with Coulomb Forces," Phys. Rev. Lett. 22, 63 (1969). | |
O. Penrose and E. R. Smith, "Thermodynamic Limit for Classical Systems with Coulomb Interactions in a Constant External Field," Comm. Math. Phys. 26, 53 (1972). | |
Foundations of Classical Statistics - General |
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M. H. Lee, "Ergodic Theory, Infinite Products and Long Time Behavior in Hermitian Models," Phys. Rev. Lett. 87, 250601 (2001). | |
E. T. Jaynes, "Where Do We Stand on Maximum Entropy," in R. D. Levine and M. Tribus, eds., The Maximum Entropy Formalism (MIT, 1979). | |
Y. Tikochinsky, N. Z. Tishby and R. D. Levine, "Consistent Inference of Probabilities for Reproducible Experiments," Phys. Rev. Lett. 52, 1357 (1984). | |
S. Nosé, "A Unified Formulation of the Constant Temperature Molecular Dynamics Methods," J. Chem. Phys. 81, 511 (1984). | |
A. Shimony, "Comment on 'Consistent Inference of Probabilities for Reproducible Experiments,'" Phys. Rev. Lett. 55, 1030 (1985). | |
Y. Tikochinsky, N. Z. Tishby and R. D. Levine, "Tikochinsky, Tishby and Levine Reply," Phys. Rev. Lett. 55, 1031 (1985). | |
Miscellaneous Formulations of Classical Statistics |
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H. Grad, Comm. Pure Appl. Math. 5, 455 (1952). | |
F. Bopp, Z. Nat. 8a, 233 (1953). | |
A. Münster, Z. Phys. 137, 386 (1954). | |
Special Problems in Classical Statistics |
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N. L. Balazs, "Statistical Mechanics of Strings," Phys. Rev. 113, 1178 (1959). | |
T. L. Hill and S. Greenschlag, "Statistical Mechanics of Monatomic Systems in an External Periodic Potential Field. I. Introduction, Virial Expansion and Classical Second Virial Coefficient," J. Chem. Phys. 34, 1538 (1961). | |
T. L. Hill and N. Saito, "Statistical Mechanics of Monatomic Systems in an External Periodic Potential Field. II. Distribution Function Theory for Fluids," J. Chem. Phys. 34, 1538 (1961). | |
A. Lenard, "Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces," J. Math. Phys. 2, 682 (1961). | |
S. F. Edwards and A. Lenard, "Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces. II. The Method of Functional Integration," J. Math. Phys. 3, 778 (1961). | |
A. Lenard, "Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces. III. Statistics of the Electric Field," J. Math. Phys. 4, 533 (1963). | |
A. Børs, "Statistical Mechanics of Rotating Systems," Z. Phys. 187, 221 (1965). | |
S. F. Edwards, "Statistical Mechanics with Topological Constraints. I.," Proc. Phys. Soc. 91, 513 (1967). | |
E. Lieb, in Mathematical Methods in Solid State and Superfliud Theory, ed. by R. C. Clarak and G. H. Derrick (Plenum, 1968). | |
L. A. Bunimovich and Y. G. Sinai, "Statistical Properties of Lorentz Gas with Periodic Configuration of Scatterers," Comm. Math. Phys. 78, 479 (1981). | |
Miscellaneous Properties of General Ensembles |
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C. Jarzynsky, "Multiple-Time-Scale Approach to Ergodic Adiabatic Systems: Another look," Phys. Rev. Lett. 71, 839 (1993). | |
C. Jarzynsky, "Nonequlibrium Equality for Free Energy Differences," Phys. Rev. Lett. 78, 2690 (1997). | |
M. Lax, "Relation Between Canonical and Microcanonical Ensembles," Phys. Rev. 97, 1419 (1955). | |
R. Kubo, J. Phys. Soc. Jpn. 17, 1100 (1962). | |
R. M. Mazo, "Free Energy of a System with Random Elements," J. Chem. Phys. 39, 1224 (1963). | |
XXX, Proc. Phys. Soc. A 1, 539 (1968). | |
D. W. Robinson and D. Ruelle, "Mean Entropy of States in Classical Statistical Mechanics," Comm. Math. Phys. 5, 288 (1967). | |
F. Henin and I. Prigogine, "Entropy, Dynamics and Molecular Chaos," Proc. Natl. Acad. Sci. 71, 2618 (1974). | |
A. Ostebee, P. Gambardella and M. Dresden, "Nonstandard Approach to the Thermodynamic Limit," Phys. Rev. A 13, 878 (1976). | |
J. T. Chayes, L. Chayes and E. Lieb, Comm. Math. Phys. 93, 57 (1984). | |
J. T. Chayes and L. Chayes, "On the Validity of the Inverse Conjecture in Classical Density Functional Theory," J. Stat. Phys. 36, 471 (1984). | |
Ergodicity of Illustrated Systems |
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J. Ford, Adv. Chem. Phys. 24, 155 (1973). | |
J. Bivins, N. Metropolis and J. Pasta, J. Comput. Phys. 12, 65 (1973). | |
B. Chirikov, F. Izrailev and V Tayurskii, Comp. Phys. Comm. 5, 11 (1973). | |
C. F. Discoll and T. M. O'Neil, "Explanation of Instabilities Observed on a Fermi-Pasta-Ulam Lattice," Phys. Rev. Lett. 37, 69 (1976). | |
General Equilibrium Theorems of Interacting Particles |
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I. Oppenheim and P. Mazur, "Density Expansions of Distribution Functions," Physica 23, 197, 216 (1957). | |
I. P. Bazarov, Zh. Eksp. Teor. Fiz. 32, 1065 (1957). | |
I. P. Bazarov, Zh. Eksp. Teor. Fiz. 32, 1163 (1957). | |
B. Zumino, "Formal Solution of the Equations of Statistical Equilibrium," Phys. Fluids 2, 20 (1959). | |
T. Morita, Prog. Theor. Phys. 21, 501 (1959). | |
A. A. Vedenov, Dokl. Akad. Nauk SSSR 125, 757 (1959). | |
T. L. Hill, "Exact Definition of Quasi-Thermodynamic Point functions in Statistical Mechanics," J. Chem. Phys. 30, 1521 (1957). | |
R. Abe, Prog. Theor. Phys. 22, 213 (1959). | |
G. E. Uhlenbeck, "Successive Approximation Methods in Classical Statistical Mechanics," Physica 26 (Suppl. 1), S17 (1960). | |
R. K. Pathria and M. P. Kawatra, "Quantum Mechanics of a Many-Body System with Square-Well Interaction," Prog. Theor. Phys. 27, 638 (1962). | |
R. Kubo, "Generalized Cumulant Expansion Method," J. Phys. Soc. Jpn. 17, 1100 (1962). | |
E. Meeron, "Indirect Exponential Coupling in the Classical Many-Body Problems," Phys. Rev. 126, 883 (1962). | |
J. K. Percus, "Approximation Methods in Classical Statistical Mechanics," Phys. Rev. Lett. 8, 462 (1962). | |
C. de Dominicis, "Variational Formulations of Equilibrium Statitical Mechanics," J. Math. Phys. 3, 983 (1962). | |
D. Ruelle, "Classical Staitstical Mechanics," Helv. Phys. Acta 36, 183 (1963). | |
E. Lieb, "New Method in the Theory of Imperfect Gases and liquids," J. Math. Phys. 4, 67 (1963). | |
O. Penrose, "The Remainder in Mayer's Fugacity Series," J. Math. Phys. 4, 1488 (1963). | |
M. D. Girardeau, "Variational Method for Classical Statistical Mechanics," J. Chem. Phys. 40, 899 (1964). | |
G. V. Ramanathan, "A New Cluster Scheme in Statistical Physics," J. Math. Phys. 7, 1507 (1966). | |
F. A. Blood, Jr., "The r-Particle Distribution Function in Classical Physics," J. Math. Phys. 7, 1613 (1966). | |
P. Ziesche, "Clusterentwicklung der Informationsgrößen im Besetzungszahl-Formalismus der klassischen Gleichgewichts-Statistik," Comm. Math. Phys. 5, 191 (1967). | |
G. Gallavotti and S. Miracle-Sole, "Statistical Mechanics of Lattice Systems," Comm. Math. Phys. 5, 317 (1967). | |
J. van der Linden, Physica, 38, 173 (1968). | |
P. Quass, K. Voss and P. Ziesche, Acta Phys. Hung. 24, 45 (1968). | |
R. B. Griffiths, "Free Energy of Interacting Magnetic Dipoles," Phys. Rev. 176, 655 (1968). | |
D. Ruelle, "Statistical Mechanics of a One-Dimensional Lattice Gas," Comm. Math. Phys. 9, 267 (1968). | |
E. Meeron, "Convergence of Coupline-Parameter Expansions for Distribution and Thermodynamic Functions," Phys. Rev. Lett. 22, 925 (1969). | |
D. Ruelle, Rigorous Results in Statistical Mechanics (Benjamin, 1969). | |
Approach to Equilibrium - H Theorem |
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A. J. Siegert, "On the Approach to Statistical Equilibrium," Phys. Rev. 76, 1708 (1949). | |
M. S. Green, "Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena," J. Chem. Phys. 20, 1281 (1952). | |
D. ter Haar and C. D. Green, "A Statistical Aspect of Boltzmann's H-Theorem," Proc. Phys. Soc. 66A, 153 (1953). | |
D. ter Haar and C. D. Green, Proc. Camb. Phil. Soc. 51, 141 (1955). | |
M. Kac in Proc. 3rd Berkeley Symposium on Mathematical Statistics and Probability (U. of California, 1955), p. 186. | |
R. Brout and I. Prigogine, Physica 22, 35 (1956). | |
M. J. Klein, "Entrology and the Ehrenfest Urn Model," Physica 22, 569 (1956). | |
M. J. Klein, "Generalization of the Ehrenfest Urn Model," Phys. Rev. 103, 17 (1956). | |
E. Teramoto, Prog. Theor. Phys. 15, 480 (1956). | |
N. Bogoliubov, J. Phys. USSR 10, 265 (1946). | |
E. T. Jaynes, "Information Theory and Statistical Mechanics," Phys. Rev. 106, 620 (1957). | |
E. T. Jaynes, "Information Theory and Statistical Mechanics II," Phys. Rev. 108, 171 (1957). | |
J. Ford, "Approach of One-Dimensional Systems to Equilibrium," Phys. Rev. 112, 1445 (1958). | |
S. A. Rice, "On a Relation Between Coarse Graining and Diagonal Singularity," J. Chem. Phys. 30, 587 (1959). | |
J. M. Blatt, Prog. Theor. Phys. 22, 745 (1959). | |
P. G. Bergmann and E. Morris, Ann. Phys. (N.Y.) 8, 266 (1959). | |
P. H. E. Meijer and J. I. Bowen, Physica 26, 478, 485 (1960). | |
I. Prigogine and F. Henin, "On the General Theory of the Approach to Equilibrium. I. Interacting Normal Modes," J. Math. Phys. 1, 349 (1960). | |
S. Teitler and R. F. Wallis, "Liouville Equation and the Resolvent Formalism," J. Math. Phys. 1, 372 (1960). | |
F. Henin, P. Résibois and F. Andrews, "On the General Theory of the Approach to Equilibrium. II. Interacting Particles," J. Math. Phys. 2, 68 (1961). | |
F. C. Andrews, "On the General Theory of the Approach to Equilibrium. III. Inhomogeneous Systems," J. Math. Phys. 2, 91 (1961). | |
J. E. Mayer, "Approach to Thermodynamic Equilibrium," J. Chem. Phys. 34, 1207 (1961). | |
N. G. Van Kampen, "A Power Series Expansion of the Master Equation," Can. J. Phys. 39, 551 (1961). | |
D. K. C. MacDonald, "Some Remarks on the Boltzmann and Anti-Boltzmann Equations," Phil. Mag. 6, 1407 (1961). | |
R. Balescu, Physica 27, 693 (1962). | |
K. Haubold, Physica 28, 834 (1962). | |
H. Gabriel, Physica 28, 1294 (1962). | |
T. Morimoto, J. Phys. Soc. Jpn. 18, 3328 (1963). | |
D. Pfirsch and S. Priess, Z. Nat. 20a, 756 (1965). | |
E. T. Jaynes, "Gibbs vs Boltzmann Entropies," Am. J. Phys. 33, 391 (1965). | |
K. Urbanik, "The Values at the Fixed Moment of Generalized Stochastic Processes," Acta Phys. Pol. 14, 577 (1965). | |
E. D. Banta, "Modification of the Ehrenfest Model in Statistical Mechanics," J. Math. Phys. 8, 387 (1967). | |
H. P. KcKean, "Speed of Approach to Equilibrium for Kac's Caricature of a Maxwellian Gas," Arch. Rat. Mech. Anal. 21, 343 (1966). | |
S. Harris, "Proof That Successive Derivatives of Boltzmann's H Function for a Discrete Velocity Gas Alternate in Sign," J. Math. Phys. 8, 2407 (1967). | |
H. S. Robertson and M. A. Huerta, "Approach to Equilbrium of Coupled, Harmonically Bound Oscillator Systems," Phys. Rev. Lett. 23, 825 (1969). | |
C. Kittel, "Postulational Basis of the Law of Increase of Entropy," Proc. Natl. Acad. Sci. 68, 2746 (1971). | |
M. W. P. Strandberg and J. R. Shane, "General Properties of Thermal-Relaxation Rate Equations," Phys. Rev. B 7, 4809 (1973). | |
F. Henin and I. Prigogine, "Entropy, Dynamics and Molecular Chaos," Proc. Natl. Acad. Sci. 71, 2618 (1974). | |
V. Bobylev, Dolk. Akad. Nauk SSSR 20, 1296 (1975) [Sov. Phys. Dokl. 20, 822 (1976). | |
M. Krook and T.-S. Wu, "Formation of Maxwellian Tails," Phys. Rev. Lett. 36, 1107 (1976). | |
M. Krook and T.-S. Wu, "Exact Solutions of the Boltzmann Equation," Phys. Fluids 20, 1589 (1977). | |
P. Résibois, "H Theorem for the (Modified) Nonlinear Enskog Equation," Phys. Rev. Lett. 40, 1409 (1978). | |
R. M. Ziff, "New Class of Soluble-Model Boltzmann Equations," Phys. Rev. Lett. 45, 306 (1980). | |
R. M. Ziff, S. D. Merajver and G. Stell, "Approach to Equilibrium of a Boltzmann-Equation Solution," Phys. Rev. Lett. 47, 1493 (1981). | |
E. Lieb, "Comment on: Approach to Equilibrium of a Boltzmann-Equation Solution," Phys. Rev. Lett. 48, 1057 (1982). | |
M. C. Mackey, "The Dynamic Origin of Increasing Entropy," Rev. Mod. Phys. 61, 981 (1989). | |
Theory of Fluctuations |
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J. Logan and M. Kac, "Fluctuations and the Boltzmann Equation," Phys. Rev. A 13, 458 (1976). | |
R. A. Medina and J. W. Garland, "General Relationship Between Concentration Derivatives and Correlation Functions for Alloys," Phys. Rev. B 14, 5060 (1976). | |
M. Smoluchowski, Ann. Phys. 25, 205 (1908). | |
L. S. Ornstein and F. Zernicke, Proc. Acad. Sci. Amsterdam 17, 793 (1914). | |
L. S. Ornstein and F. Zernicke, Proc. Acad. Sci. Amsterdam 18, 1520 (1916). | |
L. S. Ornstein and F. Zernicke, Proc. Acad. Sci. Amsterdam 19, 1321 (1917). | |
L. S. Ornstein and F. Zernicke, Physik Z. 19, 134 (1918). | |
L. S. Ornstein and F. Zernicke, Physik Z. 27, 761 (1926). | |
J. Rocard, J. de Phys. 4, 165 (1933). | |
M. J. Klein and L. Tisza, RLE Tech. Rep. 111 (1949). | |
M. J. Klein and L. Tisza, "Theory of Critical Fluctuations," Phys. Rev. 76, 1861 (1949). | |
H. B. Callen and T. A. Welton, "Irreversibility and Generalized Noise," Phys. Rev. 76, 1861 (1949). | |
H. Takahashi, J. Phys. Soc. Jpn. 7, 439 (1952). | |
J. Hashitsume, Prog. Theor. Phys. 8, 461 (1952). | |
M. Leontobich and S. M. Ritov, Zh. Eksp. Teor. Fiz. 23, 246 (1952). | |
S. M. Ritov, Dokl. Akad. Nauk SSSR 87, 535 (1952). | |
R. F. Greene and H. B. Callen, "On a Theorem of Irreversible Thermodynamics," Phys. Rev. 88, 1387 (1952). | |
C. D. Greene and D. ter Haar, Physica 21, 63 (1955). | |
M. Lax, "Fluctuations from the Nonequilibrium Steady State," Rev. Mod. Phys. 32, 25 (1960). | |
N. G. Van Kampen, "Thermal Fluctuations in Nonlinear Systems," J. Math. Phys. 4, 190 (1963). | |
J. Hori, J. Phys. Soc. Jpn. 11, 1120 (1956). | |
S. M. Ritov, Zh. Eksp. Teor. Fiz. 33, 166 (1957). | |
V. E. Matalinskii and Y. P. Terletskii, Zh. Eksp. Teor. Fiz. 34, 729 (1958). | |
E. W. Hart, "Thermodynamic Theory of the Pair Correlation Function," J. Chem. Phys. 34, 1471 (1961). | |
G. L. Jones, "Method for Treating Fluctuations of Dynamical Variables," J. Math. Phys. 6, 106 (1965). | |
G. L. Jones and M. Davies, "Fluctuations in Equlibrium and Nonequilibrium Ensembles," J. Math. Phys. 6, 1009 (1965). | |
J. A. McLennan, Helv. Phys. Acta 40, 645 (1967). | |
Theory of Brownian Motion |
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M. von Smolochowski, Abhandlungen über die Brownishe Bewegung (Akademische Verlags Gesellschaft, (1926). | |
G. E. Uhlenbeck and L. S. Ornstein, "On the Theory of Brownian Motion," Phys. Rev. 36, 823 (1930). | |
Ming Chen Wang and G. E. Uhlenbeck, "On the Theory of Brownian Motion II," Rev. Mod. Phys. 17, 373 (1945). | |
S. Chandrasekhar, "Stochastic Problems in Physics and Astronomy," Rev. Mod. Phys. 15, 1 (1943). | |
H. A. Kramers, "Brownian Motion in a Field of Force and Diffusion Model of Chemical Reactions," Physica 7, 284 (1940). | |
S. O. Rice, "Mathematical Analysis of Random Noise," Bell Syst. Tech. J. 23/b>, 282 (1944). | |
S. O. Rice, "Mathematical Theory of Random Noise," Bell Syst. Tech. J. 25/b>, 46 (1945). | |
M. Kac, "Random Walk and the Theory of Brownian Motion," Am. Math. Monthly 54/b>, 396 (1947). | |
A. Einstein, "Die von der Molekularkinetischen Theorie der W ärme geforderte Bewegung von in ruhenden Flüssigkeiten Suspendierten Teilchen," Ann. d. Phys. 17, 549 (1905). | |
R. T. Cox, "Brownian Motion in the Theory of Irreversible Processes," Rev. Mod. Phys. 24, 312 (1952). | |
M. Toda, "Theorie der Brownishen Begewung," J. Phys. Soc. Jpn. 12, 1266 (1958). | |
R. W. Zwanzig, "Contribution to the Theory of Brownian Motion," Phys. Fluids 2, 12 (1959). | |
N. Wax, ed., Selected Papers on Noise and Stochastic Processes (Dover, 1954). | |
M. S. Giterman and M. E. Gertsenshtein, Zh. Eksp. Teor. Fiz. 50, 1084 (1966) [Sov. Phys. JETP 23, 722 (1966)]. | |
R. Kubo, Rep. Prog. Phys. 29, 225 (1966). | |
J. H. Williamson, "Brownian Motion of Electrons," J. Phys. A 1, 629 (1968). | |
P. Fulde, L. Pietronero, W. R. Schneider and S. Strässler, "Problem of Brownian Motion in a Periodic Potential," Phys. Rev. Lett. 35, 1776 (1975). | |
J. R. Mehaffey and R. I. Cukier, "Kinetic-Theory Derivation of the Einstein-Stokes Law," Phys. Rev. Lett. 38, 1039 (1977). | |
S. E. Trullinger et al., "Brownian Motion of Coupled Nonlinear Oscillators: Thermalized Solitons and Nonlinear Response to External Forces," Phys. Rev. Lett. 40, 206 (1978). | |
L. E. Reichl, "Translational Brownian Motion in a Fluid with Internal Degrees of Freedom," Phys. Rev. A 24, 1609 (1981). | |
L. E. Reichl, "Effect of Fluid Rotational Degrees of Freedom on Brownian Motion: Estimates for Water," Phys. Rev. Lett. 49, 85 (1982). | |
P. Hänggi and P. Talkner, "Memory Index of First-Passage Time: A Simple Measure of Non-Markovian Character," Phys. Rev. Lett. 51, 2242 (1983). | |
J. G. Powles and N. Quirke, "Fractal Geometry and Brownian Motion: A New Parameter to Describe Molecular Motion," Phys. Rev. Lett. 52, 1517 (1984). | |
D. C. Rapaport, "Fractal Dimensionality of Brownian Motion," Phys. Rev. Lett. 53, 1965 (1984). | |
A. J. C. Ladd, M. E. Colvin and D. Frenkel, "Application of Lattice-Gas Cellular Automata to the Brownian Motion of Solids in Suspension," Phys. Rev. Lett. 60, 975 (1988). | |
G. Ryskin, "Brownian Motion in a Rotating Fluid: Diffusivity is a Function of the Rotation Rate," Phys. Rev. Lett. 61, 1442 (1988). | |
L. E. Reichl, Z.-Y. Chen and M. Millonas, "Stochastic Manifestation of Chaos in a Fokker-Planck Equation," Phys. Rev. Lett. 63, 2013 (1989). | |
R. Metzler, E. Barkai and J. Klafter, "Anomalous Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional Fokker-Planck Equation Approach," Phys. Rev. Lett. 82, 3563 (1999). | |
General Theory of Noise |
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F. N. H. Robinson, Proc. Roy. Soc. A 286, 525 (1965). | |
M. Lax, "Fluctuations from the Nonequilibrium Steady State," Rev. Mod. Phys. 32, 25 (1960). | |
M. Lax, "Classical Noise III. Nonlinear Markoff Processes," Rev. Mod. Phys. 38, 359 (1966). | |
M. Lax, "Classical Noise IV. Langevin Models," Rev. Mod. Phys. 38, 541 (1966). | |
P. T. Landsberg and E. A. B. Cole, "The Steady-State Fluctuation-Dissipation Theorem," Phys. Rev. 37, 309 (1967). | |
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