Paradoxes in the Boltzmann kinetic theory

C. Y. Chen

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Paradoxes in the Boltzmann kinetic theory

C. Y. Chen

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Abstract

Paradoxes in the Boltzmann kinetic theory are presented. Firstly, it is pointed out that the usual notion concerning the perfect continuity of distribution function is not generally valid; in many important situations using certain types of discontinuous distribution functions is an absolute must. Secondly, it is revealed that there is no time reversibility in terms of beam-to-beam collisions and, in connection with this, there are intrinsic difficulties in formulating the net change of molecular density due to collisions, either in the three-dimensional velocity space or in the six-dimensional phase space. With help of simple examples, the paradoxes manifest themselves clearly.

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C. Y. Chen. 2003-12-08. Paradoxes in the Boltzmann kinetic theory. https://arxiv.org/abs/physics/0312043

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