Collisionless kinetic theory of rolling molecules

Details Collisionless kinetic theory of rolling molecules Collisionless kinetic theory of rolling molecules

2011-09-28

arxiv.org/abs/1109.6365v2

Nonlinear Sciences

Chaotic Dynamics

Revised version; 30 pages, 1 figure

Scientific paper

We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of statistical physics. In particular, we show that even though the energy of the system is conserved, and the system is closed in the thermodynamic sense, some fundamental features of statistical physics such as invariant measure do not hold for such nonholonomic systems. Nevertheless, we are able to construct a consistent kinetic theory using Hamilton's variational principle in Lagrangian variables, by regarding the kinetic solution as being concentrated on the constraint distribution. A cold fluid closure for the kinetic system is also presented, along with a particular class of exact solutions of the kinetic equations.

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