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The existence of more than one steady-state in a many-body quantum system driven out-of-equilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this Letter, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady-state exists regardless of the initial electronic preparation of the quantum dot consistent with the converged numerical results. However, a bistability can be observed for different initial phonon preparations. The effects of the phonon frequency and strength of the electron-phonon couplings on the relaxation to steady-state and on the emergence of bistability is discussed.

Over 80% of diffuse intrinsic pontine gliomas (DIPGs) harbor a point mutation in histone H3.3 where lysine 27 is substituted with methionine (H3.3K27M); however, how the mutation affects kinetics and function of PcG proteins remains elusive. We demonstrate that H3.3K27M prolongs the residence time and search time of Ezh2, but has no effect on its fraction bound to chromatin. In contrast, H3.3K27M has no effect on the residence time of Cbx7, but prolongs its search time and decreases its fraction bound to chromatin. We show that increasing expression of Cbx7 inhibits the proliferation of DIPG cells and prolongs its residence time. Our results highlight that the residence time of PcG proteins directly correlates with their functions and the search time of PcG proteins is critical for regulating their genomic occupancy. Together, our data provide mechanisms in which the cancer-causing histone mutation alters the binding and search dynamics of epigenetic complexes.