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Competing Interests: Declaration of interests We declare no competing interests.

Background: nationally determined contributions (NDCs) serve to meet the goals of the Paris Agreement of staying "well below 2°C", which could also yield substantial health co-benefits in the process. However, existing NDC commitments are inadequate to achieve this goal. Placing health as a key focus of the NDCs could present an opportunity to increase ambition and realise health co-benefits. We modelled scenarios to analyse the health co-benefits of NDCs for the year 2040 for nine representative countries (ie, Brazil, China, Germany, India, Indonesia, Nigeria, South Africa, the UK, and the USA) that were selected for their contribution to global greenhouse gas emissions and their global or regional influence., Methods: Modelling the energy, food and agriculture, and transport sectors, and mortality related to risk factors of air pollution, diet, and physical activity, we analysed the health co-benefits of existing NDCs and related policies (ie, the current pathways scenario) for 2040 in nine countries around the world. We compared these health co-benefits with two alternative scenarios, one consistent with the goal of the Paris Agreement and the Sustainable Development Goals (ie, the sustainable pathways scenario), and one in line with the sustainable pathways scenario, but also placing health as a central focus of the policies (ie, the health in all climate policies scenario)., Findings: Compared with the current pathways scenario, the sustainable pathways scenario resulted in an annual reduction of 1·18 million air pollution-related deaths, 5·86 million diet-related deaths, and 1·15 million deaths due to physical inactivity, across the nine countries, by 2040. Adopting the more ambitious health in all climate policies scenario would result in a further reduction of 462 000 annual deaths attributable to air pollution, 572 000 annual deaths attributable to diet, and 943 000 annual deaths attributable to physical inactivity. These benefits were attributable to the mitigation of direct greenhouse gas emissions and the commensurate actions that reduce exposure to harmful pollutants, as well as improved diets and safe physical activity., Interpretation: A greater consideration of health in the NDCs and climate change mitigation policies has the potential to yield considerable health benefits as well as achieve the "well below 2°C" commitment across a range of regional and economic contexts., Funding: This work was in part funded through an unrestricted grant from the Wellcome Trust (award number 209734/Z/17/Z) and supported by an Engineering and Physical Sciences Research Council grant (grant number EP/R035288/1)., (Copyright © 2021 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license. Published by Elsevier Ltd.. All rights reserved.)

Translations: For the Chinese, French, German, and Spanish translations of the abstract see Supplementary Materials section., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

A central question of dynamics, largely open in the quantum case, is to what extent it erases a system's memory of its initial properties. Here we present a simple statistically solvable quantum model describing this memory loss across an integrability-chaos transition under a perturbation obeying no selection rules. From the perspective of quantum localization-delocalization on the lattice of quantum numbers, we are dealing with a situation where every lattice site is coupled to every other site with the same strength, on average. The model also rigorously justifies a similar set of relationships, recently proposed in the context of two short-range-interacting ultracold atoms in a harmonic waveguide. Application of our model to an ensemble of uncorrelated impurities on a rectangular lattice gives good agreement with ab initio numerics.