A calculable and quasi-practical gas

A new kinetic approach is developed and a quasi-practical gas is defined to which the new approach can be applied. One of the advantages of this new approach over the standard one is direct calculability in terms of today's computational means.Comment: 12 pages, 6 figures, late

Paradoxical aspects of the kinetic equations

Two paradoxical aspects of the prevailing kinetic equations are presented. One is related to the usual understanding of distribution function and the other to the usual understanding of the phase space. With help of simple counterexamples and direct analyses, involved paradoxes manifest themselves.Comment: 9 pages, Late

A path-integral approach to the collisional Boltzmann gas

Collisional effects are included in the path-integral formulation that was proposed in one of our previous paper for the collisionless Boltzmann gas. In calculating the number of molecules entering a six-dimensional phase volume element due to collisions, both the colliding molecules and the scattered molecules are allowed to have distributions; thus the calculation is done smoothly and no singularities arise.Comment: 18 pages, 11 figure

Mathematical investigation of the Boltzmann collisional operator

Problems associated with the Boltzmann collisional operator are unveiled and discussed. By careful investigation it is shown that collective effects of molecular collisions in the six-dimensional position and velocity space are more sophisticated than they appear to be.Comment: 5 pages, 1 figure

Counterexamples of Boltzmann's equation

To test kinetic theories, simple and practical setups are proposed. It turns out that these setups cannot be treated by Boltzmann's equation. An alternative method, called the path-integral approach, is then employed and a number of ready-for-verification results are obtained.Comment: 17 pages, 6 figures, theoretical analyses have been moved to appendixe

A new uncertainty principle

By examining two counterexamples to the existing theory, it is shown, with mathematical rigor, that as far as scattered particles are concerned the true distribution function is in principle not determinable (indeterminacy principle or uncertainty principle) while the average distribution function over each predetermined finite velocity solid-angle element can be calculated.Comment: 12 pages, 7 figure

Boltzmann's H-theorem and time irreversibility

It is shown that the justification of the Boltzman H-theorem needs more than just the assumption of molecular chaos and the picture of time irreversibility related to it should be reinvestigated.Comment: 7 pages, 3 figures, changes in languag

Nonexistence of time reversibility in statistical physics

Contrary to the customary thought prevailing for long, the time reversibility associated with beam-to-beam collisions does not really exist. Related facts and consequences are presented. The discussion, though involving simple mathematics and physics only, is well-related to the foundation of statistical theory.Comment: 10 pages, 5 figures, late

A counterexample against the Vlasov equation

A simple counterexample against the Vlasov equation is put forward, in which a magnetized plasma is perturbed by an electromagnetic standing wave.Comment: 5 pages, 1 figur

Paradoxes in the Boltzmann kinetic theory

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.Comment: 18 pages, 10 figures, late