On the quantum-statistical ergodic and H -theorems

Abstract

Metrical indecomposability is a condition for the validity of the classical ergodic theorem. Its counterpart in the quantum-statistical theorem is believed to be non-degeneracy of the energy eigenvalues. It is shown here, however, that the coarse-grained quantum-statistical theorems (due to von Neumann and to Pauli & Fierz) remain valid in the presence of energy degeneracy. This requires, therefore, a reassessment of the significance of these theorems; this is discussed, and it is concluded that the von Neumann approach is unsatisfactory in that it fails to yield a microscopic criterion for either ergodicity or validity of the H -theorem.