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The Marolf-Maxfield topological toy model for 2D gravity gives the fullspectrum of boundary theories, but can not describe any evolution. In order toobtain the expected evolution from Hartle-Hawking state to one of thesuperselection sectors, we suggest to consider a correspondence between modelsof evaporating black holes and models of collapsing wave functions. This noteexplores this correspondence by equating the Marolf-Maxfield topological toymodel and to the Bonifacio model of spontaneous collapse theory. The expectedevolution of a matrix element due to a generator of a parameter inMarolf-Maxfield model is obtained.

Proposed evolution in Marolf-Maxfield toy model obtained through correspondence to spontaneous collapse theory