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The outcomes of measurements on entangled quantum systems can be nonlocally correlated. However, while it is easy to write down toy theories allowing arbitrary nonlocal correlations, those allowed in quantum mechanics are limited. Quantum correlations cannot, for example, violate a principle known as macroscopic locality, which implies that they cannot violate Tsirelson’s bound. This paper shows that there is a connection between the strength of nonlocal correlations in a physical theory and the structure of the state spaces of individual systems. This is illustrated by a family of models in which local state spaces are regular polygons, where a natural analogue of a maximally entangled state of two systems exists. We characterize the nonlocal correlations obtainable from such states. The family allows us to study the transition between classical, quantum and super-quantum correlations by varying only the local state space. We show that the strength of nonlocal correlations—in particular whether the maximally entangled state violates Tsirelson’s bound or not— depends crucially on a simple geometric property of the local state space, known as strong self-duality. This result is seen to be a special case of a general theorem, which states that a broad class of entangled states in probabilistic theories—including, by extension, all bipartite classical and quantum states— cannot violate macroscopic locality. Finally, our results show that models exist that are locally almost indistinguishable from quantum mechanics, but can nevertheless generate maximally nonlocal correlations.
Using the particle-resolved aerosol model PartMC-MOSAIC, we simulate the heterogeneous oxidation of a monolayer of polycyclic aromatic hydrocarbons (PAHs) on soot particles in an urban atmosphere. We focus on the interaction of the major atmospheric oxidants (O3, NO2, OH, and NO3) with PAHs and include competitive co-adsorption of water vapour for a range of atmospheric conditions. For the first time detailed heterogeneous chemistry based on the P¨oschl-Rudich-Ammann (PRA) framework is modelled on soot particles with a realistic size distribution and a continuous range of chemical ages. We find PAH half-lives, 1/2, on the order of seconds during the night, when the PAHs are rapidly oxidised by the gas-surface reaction with NO3. During the day, 1/2 is on the order of minutes and determined mostly by the surface layer reaction of PAHs with adsorbed O3. Such short half-lives of surface-bound PAHs may lead to efficient conversion of hydrophobic soot into more hygroscopic particles, thus increasing the particles’ aerosol-cloud interaction potential. Despite its high reactivity OH appears to have a negligible effect on PAH degradation which can be explained by its very low concentration in the atmosphere. An increase of relative humidity (RH) from 30% to 80% increases PAH half-lives by up to 50%for daytime degradation and by up to 100% or more for nighttime degradation. Uptake coefficients, averaged over the particle population, are found to be relatively constant over time for O3 (2×10-7 to 2×10-6) and NO2 (5×10-6 to 10-5) at the different levels of NOx emissions and RH considered in this study. In contrast, those for OH and NO3 depend strongly on the surface concentration of PAHs. We do not find a significant influence of heterogeneous reactions on soot particles on the gas phase composition. The derived half-lives of surfacebound PAHs and the time and particle population averaged uptake coefficients for O3 and NO2 presented in this paper can be used as parameterisations for the treatment of heterogeneous chemistry in large-scale atmospheric chemistry models.