Abstract
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 nonzero, 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 behavior is interpreted in terms of noncritical Liouville string, with the Liouville field identified as the target time.
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