Brownian Motion and Nonequilibrium Statistical Mechanics

This article is a personal reflection of the branch of nonequilibrium statistical mechanics called the linear response theory that has as its heart the fluctuation-dissipation thereom, which states that irreversible processes ip nonequilibrium are necessarily related to thermal fluctuations in equilibrium. Its origi lies in the Einstein relation for the diffusion constant and the mobility of a Brownian particle. The short history of the fluctuation-dissipation theorem is described. Then the linear response theory is brifly summarized and the meaning of stochastization is considered. The Langevin equation approach and its extensions are reviewed.

[1]  J. S. Dowker,et al.  Green's Functions and Condensed Matter , 1982 .

[2]  E. Hanamura,et al.  Second order optical processes in a localized electron-phonon system- Transient response , 1978 .

[3]  E. Hanamura,et al.  Stochastic Models of Intermediate State Interaction in Second Order Optical Processes –Stationary Response. II– , 1977 .

[4]  R. Kubo.  The fluctuation-dissipation theorem , 1966 .

[5]  R. Kubo,et al.  Quantum Theory of Galvanomagnetic Effect at Extremely Strong Magnetic Fields , 1965 .

[6]  R. Kubo.  Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems , 1957 .

[7]  Ryogo Kubo,et al.  Application of the Method of Generating Function to Radiative and Non-Radiative Transitions of a Trapped Electron in a Crystal , 1955 .

[8]  Melville S. Green,et al.  Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena. II. Irreversible Processes in Fluids , 1954 .

[9]  J. Doob.  Stochastic processes , 1953 .

[10]  P. Anderson,et al.  Exchange Narrowing in Paramagnetic Resonance , 1953 .

[11]  H. Takahasi.  Generalized Theory of Thermal Fluctuations , 1952 .

[12]  Melville S. Green,et al.  Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena , 1952 .

[13]  R. Kubo.  Thermal Ionization of Trapped Electrons , 1952 .

[14]  Richard F. Greene,et al.  On a Theorem of Irreversible Thermodynamics , 1952 .

[15]  E. Purcell,et al.  Relaxation Effects in Nuclear Magnetic Resonance Absorption , 1948 .

[16]  L. Onsager.  Reciprocal Relations in Irreversible Processes. II. , 1931 .

[17]  H. Nyquist.  Thermal Agitation of Electric Charge in Conductors , 1928 .