Many advanced quantum techniques feature non-Gaussian dynamics, and the ability to manipulate the system in that domain is the next stage in many experiments. One example of meaningful non-Gaussian dynamics is that of a double-well potential. Here we study the dynamics of a levitated nanoparticle undergoing the transition from a harmonic potential to a double well in a realistic setting, subjected to both thermalization and localization. We characterize the dynamics of the nanoparticle from a thermodynamic point of view, investigating the dynamics with the Wehrl entropy production and its rates. Furthermore, we investigate coupling regimes where the the quantum effect and thermal effect are of the same magnitude, and look at suitable squeezing of the initial state that provides the maximum coherence. The effects and the competitions of the unitary and the dissipative parts onto the system are demonstrated. We quantify the requirements to relate our results to a bonafide experiment with the presence of the environment, and discuss the experimental interpretations of our results in the end.
