Hello. Do you know any textbook about Statistical Mechanics that discusses Boltzmann Transport Equation? It is not discussed in the textbooks that I know. Thank you.
http://en.wikipedia.org/wiki/Boltzmann_equation It looks like a specific case of the Reynolds transport equation, but it also appears related to "detailed balance", the Langevin model, the Smoluchowski equation, the Fokker-Planck equation... The context seems to be kinetic theory and correlation functions- I found brief discussions in Boon and Yip's "Molecular Hydrodynamics", and additional material in Chaikin and Lubensky's "Principles of Condensed Matter Physics" and Brenner and Edwards "Macrotransport Processes".
Landau & Lifschitz' <Physical Kinetics> and R. Balescu's <Nonequilibrium Statistical Mechanics> are sources on this issue. Of course, basically any textbook on nonequlibrium statistical mechanics discusses the BBGKY hierarchy and Boltzmann's equation.
One of the best books on the subject is L. Kadanoff, G. Baym, Quantum Statistical Mechanics An original paper, which however has textbook quality and uses the Schwinger-Keldysh real-time contour formulation of non-relativistic off-equilibrium quantum field theory is the publication of Pawel Danielevic's PhD-Thesis: Danielewicz, P.: Quantum Theory of Nonequilibrium Processes. 1, Ann. Phys. 152, 239, 1984 For the relativistic case and with extensions to off-shell transport, see the lecture notes by Wolfgang Cassing Cassing, W.: From Kadanoff-Baym dynamics to off-shell parton transport, Eur. Phys. J. ST 168, 3–87, 2009 For a more general approach also for the relativistic case: S. R. de Groot, W. A. van Leeuwen, Ch. G. van Weert, Relativistic kinetic theory