The Boltzmann equation for discrete systems

by R. F. Streater.

being pages 101-132 in "Statistical Mechanics", ed. Allan I Solomon, World Scientific, 1988.

This is the proceedings of the tenth annual conference on statistical mechanics, held at the Open University, Milton Keynes, England.

ABSTRACT

We explain our theory of non-linear stochastic processes, applied to the kinetic theory of adiabatic discrete systems, in the manner of Boltzmann. The theory is illustrated by some simple classical, quantum and second-quantised models. The dynamics of a system of several harmonic oscillators can be chosen to be energy-conserving and ergodic, but only if the frequencies are mutually rational. This remark relates the possibility of satisfying the first and second laws of thermodynamics to the instabilty of the underlying classical system.