Legget-Garg inequality for a quantum model of ion channels

Temporal quantum correlations, revealed by violations of the Leggett-Garg inequalities (LGIs), offer a powerful framework to probe nonclassical dynamics in conceptual models, including those inspired by the living systems. Here, we examine a three-state representation of ionic transport through the selectivity filter, previously presented by Seifi et al. Using this model, we systematically investigate how different scenarios, such as initial state preparation, the specification of measurement basis, hopping dynamics, and environmental fluctuations, affect the emergence of temporal nonclassicality. The choice of measurement basis is found to play a decisive role in shaping temporal quantum correlations. Our analysis reveals that the strongest LGI violations occur for intermediate model configurations, which represent a short-lived state where a potassium ion is poised for release while still coupled to surrounding water sites, whereas entry and exit configurations exhibit weaker quantum signatures. Static fluctuations of the hopping parameters confine LGI violations to shorter time windows, while dynamic decoherence suppresses them irrespective of the hopping amplitude. Overall, our findings demonstrate that LGI-based analyses can identify stages where temporal quantum correlations are most significant, highlighting the intermediate knock-on configuration as a promising target for future studies of intrinsically quantum effects in ion-conduction phenomena.