2003/12/08 by C. Y. Chen, Chen, C. Y.
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Machine Learning in Materials Science #physics.class-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.physics/0312043
18 pages, 10 figures, latex
arxiv created 2003/12/08 · arxiv updated 2009/12/01
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.