  We show that an exact solution of two-dimensional dilaton gravity with matter
discovered previously exhibits an irreversible temporal flow towards flat space
with a vanishing cosmological constant. This time flow is induced by the back
reaction of matter on the space-time geometry. We demonstrate that the system
is not in equilibrium if the cosmological constant is non-zero, whereas the
solution with zero cosmological constant is stable. The flow of the system
towards this stable end-point is derived from the renormalization-group flow of
the Zamolodchikov function. This behaviour is interpreted in terms of
non-critical Liouville string, with the Liouville field identified as the
target time.
