What Textbooks Cover the Boltzmann Transport Equation in Statistical Mechanics?

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Discussion Overview

The discussion revolves around identifying textbooks that cover the Boltzmann Transport Equation within the context of Statistical Mechanics. Participants explore various sources and related concepts, including kinetic theory and nonequilibrium statistical mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about textbooks discussing the Boltzmann Transport Equation, noting that it is not covered in the texts they are familiar with.
  • Another participant references a Wikipedia page and suggests that the Boltzmann equation relates to the Reynolds transport equation, detailed balance, Langevin model, Smoluchowski equation, and Fokker-Planck equation, indicating a connection to kinetic theory and correlation functions.
  • Several textbooks are proposed, including Boon and Yip's "Molecular Hydrodynamics," Chaikin and Lubensky's "Principles of Condensed Matter Physics," and Brenner and Edwards' "Macrotransport Processes," which contain brief discussions on the topic.
  • Landau & Lifschitz' "Physical Kinetics" and R. Balescu's "Nonequilibrium Statistical Mechanics" are mentioned as sources that address the Boltzmann equation and the BBGKY hierarchy.
  • Another participant highlights L. Kadanoff and G. Baym's "Quantum Statistical Mechanics" as a significant resource, along with Pawel Danielewicz's PhD thesis publication and Wolfgang Cassing's lecture notes on relativistic transport.
  • Lastly, S. R. de Groot et al.'s work on relativistic kinetic theory is noted as a more general approach to the topic.

Areas of Agreement / Disagreement

Participants present multiple viewpoints and sources regarding the Boltzmann Transport Equation, indicating that there is no consensus on a single definitive textbook or approach.

Contextual Notes

Some discussions reference related concepts and equations, but the connections and implications of these relationships remain unresolved. The scope of the textbooks mentioned varies, and the completeness of their coverage on the Boltzmann Transport Equation is not uniformly assessed.

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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.
 
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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
 

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