Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems

Journal Article · Thu Jan 05 00:00:00 EST 1995 · International Journal of Quantum Chemistry

DOI:https://doi.org/10.1002/qua.560530115· OSTI ID:482335

Prigogine, I ^[1]

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1. Univ. of Texas, Austin, TX (United States)

Nonintegrable Poincare systems with a continuous spectrum lead to the appearance of diffusive terms in the frame of classical or quantum dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory theory and of wave-function formalism. These diffusive terms correspond to well-defined classes of dynamical processes. The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include, already, in the fundamental dynamical description the two basic aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions. For integrable systems, we recover the usual formulation of classical or quantum mechanics. Instead of being primitive concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville-von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature that we inherited from the nineteenth century, based, on the one hand, on dynamical time-reversible laws and, on the other, on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory, avoiding the conventional dual structure based on Schroedinger`s equation, on the one hand, and on the {open_quotes}collapse{close_quotes} of the wave function, on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations. There is a striking parallelism between classical and quantum theory. For large Poincare systems (LPS), we have, in general, both a {open_quotes}collapse{close_quotes} of trajectories and of wave functions. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices.

• Sponsoring Organization: USDOE
• DOE Contract Number: FG05-88ER13897
• OSTI ID: 482335
• Journal Information: International Journal of Quantum Chemistry, Journal Name: International Journal of Quantum Chemistry Journal Issue: 1 Vol. 53; ISSN IJQCB2; ISSN 0020-7608
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CLASSICAL MECHANICS
IRREVERSIBLE PROCESSES
POINCARE GROUPS
QUANTUM MECHANICS
WAVE FUNCTIONS