  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.
