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Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in Kirkwood–Dirac (KD) quasiprobability distribution, the distinctive quantum mechanical feature of noncommutativity which underlies many nonclassical phenomena, manifests in the nonreal values and/or the negative values of the real part. Here, we develop a faithful quantifier of quantum coherence based on the KD nonclassicality which captures simultaneously the nonreality and the negativity of the KD quasiprobability. The KD-nonclassicality coherence thus defined, is upper bounded by the uncertainty of the outcomes of measurement described by a rank-1 orthogonal projection-valued measure (PVM) corresponding to the incoherent orthonormal basis which is quantified by the Tsallis 1 2 -entropy. Moreover, they are identical for pure states so that the KD-nonclassicality coherence for pure state admits a simple closed expression in terms of measurement probabilities. We then use the Maassen–Uffink uncertainty relation for min-entropy and max-entropy to obtain a lower bound for the KD-nonclassicality coherence of a pure state in terms of optimal guessing probability in measurement described by a PVM noncommuting with the incoherent orthonormal basis. We also derive a trade-off relation for the KD-nonclassicality coherences of a pure state relative to a pair of noncommuting orthonormal bases with a state-independent lower bound. Finally, we sketch a variational scheme for a direct estimation of the KD-nonclassicality coherence based on weak value measurement and thereby discuss its relation with quantum contextuality. [ABSTRACT FROM AUTHOR]

Pyrolyzed Fe–N–C-based catalysts, particularly FeN4, are reported to show enhanced catalytic activity for some chemical reactions, particularly for the oxygen reduction reaction (ORR). Here, we present a computational study to investigate another pyrolyzed Fe–N–C-based catalyst, i.e. Fe2N6, adsorbed on graphene with special emphasis on the edges of graphene nanoribbons (both zig-zag and armchair configurations) as a candidate for Fe dual-atom catalysts (Fe-DACs). Utilizing density functional theory calculations along with microkinetic simulations, we investigate the influence of graphitic edges on the stability and ORR activity of Fe-DAC active sites. Our findings indicate that the presence of graphitic edges, particularly the zig-zag configuration, significantly lowers the formation energy of Fe-DAC active sites, making them more likely to form at the edges. Furthermore, several Fe-DAC active sites at graphitic edges exhibit exceptional ORR performance, surpassing the commonly employed FeN4 active site in SAC systems and even exceeding the benchmark Pt(111) surface. Notably, the (Fe2N6)o@z1 active site demonstrates outstanding performance in both associative and dissociative mechanisms. These results highlight the role of graphitic nanopores in enhancing the catalytic behavior of Fe-DAC active sites, providing valuable insights for designing efficient non-precious metal catalysts for ORR applications. [ABSTRACT FROM AUTHOR]