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Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena. II. Irreversible Processes in Fluids
1.M. S. Green, J. Chem. Phys. 20, 1281 (1952).
2.S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases (Cambridge University Press, Cambridge, 1939).
3.M. Born and H. S. Green, A General Kinetic Theory of Liquids (Cambridge University Press, Cambridge, 1949).
4.J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950).
4.See also J. G. Kirkwood, J. Chem. Phys. 14, 180 (1946).
5.S. de Groot The Thermodynamics of Irreversible Processes (North Holland Publishing Company, Amsterdam, 1951).
6.By the internal energy of a system we mean its energy as it would be determined by an observer moving along with its center of mass.
7.H. Goldstein Classical Mechanics (Addison‐Wesley Press, Cambridge, Massachusetts, 1950).
8.We use the notation of partial differentiation by a vector as an abbreviation.
9.This conjecture is based on the behavior of similar quantities which appear in Peierls’ theory of heat conductivity of crystals [Ann. Physik 3, 1055 (1929)] and on the fact that in the quantum theory of scattering and of radiation, time‐proportional transition probabilities are obtained only in the limit in which the size of the system goes to infinity.
10.These are proportional to
11.S. Chandrasekhar, Revs. Modern Phys. 15, 2 (1943). This expression is not explicitly derived but is easily verified from the explicit transition probabilities for the velocity given there.
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