  In this paper, we present a concrete example that highlights how predictions
in non-Hermitian quantum mechanics can be inaccurately influenced by the
absence of environment-induced fluctuations in the model. Specifically, we
investigate the non-Hermitian skin effect and sensor in the Hatano-Nelson
model, contrasting it with a more precise Lindblad description. Our analysis
reveals that these phenomena can undergo breakdown when environmental
fluctuations come to the forefront, resulting in a non-equilibrium phase
transition from a localized skin phase to a delocalized phase. Beyond this
specific case study, we engage in a broader discussion regarding the
interpretations and implications of non-Hermitian quantum mechanics. This
examination serves to broaden our understanding of these phenomena and their
potential consequences.
