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

A path-integral approach to the collisionless Boltzmann gas

On contrary to the customary thought, the well-known ``lemma'' that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One of its consequences states that the velocity distribution at any point is a condensed ``image'' of all, complex and even discontinuous, structures of the entire spatial space. Admitting the inability to describe the entire space with a microscopic quantity, this paper introduces a new type of distribution function, called the solid-angle-average distribution function. With help of the new distribution function, the dynamical behavior of collisionless Boltzmann gas is formulated in terms of a set of integrals defined by molecular paths. In the new formalism, not only that the difficulties associated with the standard theory are surmounted but also that some of practical gases become calculable in terms of today's computer.Comment: 18 pages, 8 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