Statistical irreversibility: classical and quantum.

Geoffrey L. Sewell

N. G. van Kampen

Henry B. Hollinger, Michael John Zenzen

Vladimir S. Mashkevich

Arthur Hobson

It is shown that the usual proofs of the quasiperiodicity of isolated, finite quantum-statistical systems, previously thought to be general proofs, are in reality based on the special case of a discrete array. Quasiperiodicity is demonstrated for the analogous special case (the discrete distribution) in classical statistical mechanics. The density-operator formalism is set up for the case of a continuous array. The question of the possibly irreversible behavior of isolated, finite quantum-statistical systems with continuous arrays is investigated. An argument is given indicating that such systems generally behave irreversibly. The situations in classical and quantum statistics then appear to be entirely analogous, since it is well known that isolated, finite classical-statistical systems may, in the case of a continuous distribution (the analog of a continuous quantum-statistical array), behave irreversibly.

Yutaka Toyozawa

Arguments are presented for the viewpoint that irreversibility is inherent in quanturn mechanics, irrespective of the number of particles participating. This fact is related to the notion of transition–ramifying evolution–which is characteristic of quantum mechanics. It is in contrast to classical mechanics based on the notion of orbit, where the irreversibility arises only as the result of a large number of particles or a certain complexity of the system. The statistical assumption needed for the derivation of irreversibility in classical mechanics is absorbed into the uncertainty principle of quantum mechanics, and is revived as inherent irreversibility. The statements conform with the parallelism of quantum mechanics and classical statistical mechanics emphasized in a previous report.