Fundamental link between system theory and statistical mechanics

Journal Article · Tue Sep 01 04:00:00 EDT 1987 · Found. Phys.; (United States)

DOI:https://doi.org/10.1007/BF00734321· OSTI ID:5267390

Atmanspacher, H; Scheingraber, H

A fundamental link between system theory and statistical mechanics has been found to be established by the Kolmogorov entropy. By this quantity the temporal evolution of dynamical systems can be classified into regular, chaotic, and stochastic processes. Since K represents a measure for the internal information creation rate of dynamical systems, it provides an approach to irreversibility. The formal relationship to statistical mechanics is derived by means of an operator formalism originally introduced by Prigogine. For a Liouville operator L and an information operator M tilde acting on a distribution in phase space, it is shown that i(L, M tilde) = KI (I = identity operator). As a first consequence of this equivalence, a relation is obtained between the chaotic correlation time of a system and Prigogine's concept of a finite duration of presence. Finally, the existence of chaos in quantum systems is discussed with respect to the existence of a quantum mechanical time operator.

• Research Organization: Max-Planck-Institut fuer Physik und Astrophysik (Germany, F.R.)
• OSTI ID: 5267390
• Journal Information: Found. Phys.; (United States), Journal Name: Found. Phys.; (United States) Vol. 17:9; ISSN FNDPA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMMUTATION RELATIONS
CORRELATION FUNCTIONS
DIFFERENTIAL EQUATIONS
EIGENVALUES
ENTROPY
EQUATIONS
FLUCTUATIONS
FUNCTIONS
KOLMOGOROV EQUATION
LYAPUNOV METHOD
MATHEMATICS
MEASURE THEORY
MECHANICS
NONLINEAR PROBLEMS
PHYSICAL PROPERTIES
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
THERMODYNAMIC PROPERTIES
THERMODYNAMICS
TRANSPORT THEORY
VARIATIONS