Expansion exponents for nonequilibrium systems

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 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 behavior for quasi-isolated systems results in the formulation of two other principles: The principle of asymptotic expansion tells that the phase volumes of quasi-isolated systems expand at asymptotically large times. The 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.