How large are dissipative effects in noncritical Liouville string theory?

In the context of non-critical Liouville strings, we clarify why we expect non-quantum-mechanical dissipative effects to be O(E²/MP), where E is a typical energy scale of the probe, and MP is the Planck scale. In Liouville strings, energy is conserved at best only as a statistical average, as distinct from Lindblad systems, where it is strictly conserved at an operator level, and the magnitude of dissipative effects could only be much smaller. We also emphasize the importance of nonlinear terms in the evolution equation for the density matrix, which are important for any analysis of complete positivity.