We consider an Ehrenfest approximation for a particle in a double-well potential in the presence of an external environment schematized as a finite resource heat bath. This allows us to explore how the limitations in the applicability of Ehrenfest dynamics to nonlinear systems are modified in an open system setting. Within this framework, we have identified an environment-induced spontaneous symmetry breaking mechanism, and we argue that the Ehrenfest approximation becomes increasingly valid in the limit of strong coupling to the external reservoir, either in the form of increasing number of oscillators or increasing temperature. The analysis also suggests a rather intuitive picture for the general phenomenon of quantum tunneling and its interplay with classical thermal activation processes, which may be of relevance in physical chemistry, ultracold atom physics, and fast-switching dynamics such as in superconducting digital electronics.
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