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Published online by Cambridge University Press: 05 July 2011
Where is the knowledge we have lost in information?
T.S. EliotBBGK and Y stand for the names of the physicists who independently, or in different contexts, developed a rigorous way to extract knowledge from the information in many-variable partial differential equations: Born, Bogoliubov, Green, Kirkwood and Yvon. The basic idea is to turn one equation with a large number of variables into many equations, each with a small number of variables. The many equations cannot be the orbit equations since each orbit equation contains the positions and velocities of all the other objects. Virial and higher order moment equations are useful for answering some questions, but for others they average out too much of the information. However, an hierarchial set of coupled equations involving the reduced distribution functions (10.25) may provide just the right amount of detail.
To place various approximations of the many-body problem in some perspective, Figure 10 shows the relations among their information content. Both the master equation and Liouville's equation provide independent starting points for a manybody description. Liouville's equation is completely consistent and self-contained (represented by the box around it) whereas the master equation requires further physical input before it is useful. The Langevin equation is so phenomenological as to be in a class of its own.
Arrows in Figure 10 show the direction in which information is sacrificed to obtain solvability. Information, here, is represented by the detail of the many-body description.
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