Expansion Exponents for Nonequilibrium Systems

Abstract

Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of calculating the exponents are discussed. The {\it principle of minimal expansion} provides the basis for treating the problem of pattern selection. The exponents are also defined for stochastic dynamical systems. The analysis of the expansion-exponent behaviour for quasi-isolated systems results in the formulation of two other principles: The {\it principle of asymptotic expansion} tells that the phase volumes of quasi-isolated systems expand at asymptotically large times. The {\it principle of time irreversibility} follows from the asymptotic phase expansion, since the direction of time arrow can be defined by the asymptotic expansion of phase volume.

23 pages, Latex

References in corpus (5)

• Self-Similar Extrapolation of Asymptotic Series and Forecasting for Time Series
• Principle of Pattern Selection for Nonequilibrium Phenomena
• Self-similar approach to market analysis
• Turbulent Photon Filamentation in Resonant Media
• Probabilistic Approach to Pattern Selection

Cited by in corpus (7)

• Evolutionary Processes in Quantum Decision Theory
• Nonequilibrium representative ensembles for isolated quantum systems
• Quantum decision making by social agents
• Equilibration of quasi-isolated quantum systems
• Coherent dynamics of radiating atomic systems in pseudospin representation
• Mapping the three-body system - decay time and reversibility
• Models of Mixed Matter