  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.
