IRREVERSIBLE TIME FLOW IN A 2-DIMENSIONAL DILATON BLACK-HOLE WITH MATTER

We show that an exact solution of two-dimensional dilaton gravity with matter discovered previously exhibits an irreversible temporal how to wards hat 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 cosmologi cal constant is nonzero, whereas the solution with zero cosmological c onstant is stable. The how of the system towards this stable end point is derived from the renormalization-group flow of the Zamolodchikov f unction. This behavior is interpreted in terms of noncritical Liouvill e string, with the Liouville field identified as the target time.