  A physical system is called quasi-isolated if it subject to small random
uncontrollable perturbations. Such a system is, in general, stochastically
unstable. Moreover, its phase-space volume at asymptotically large time
expands. This can be described by considering the local expansion exponent.
Several examples illustrate that the stability indices and expansion exponents
of quasi-isolated systems are not only asymptotically positive but are
asymptotically increasing. This means that the divergence of dynamical
trajectories and the expansion of phase volume at large time occurs with
acceleration. Such a strongly irreversible evolution of quasi-isolated systems
explains the irreversibility of time.
