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Engine lubricants globally face the challenge of meeting the demands of new engine technologies while enhancing energy efficiency and reducing emissions. Lubricants must enhance their performance and sustainability, improve reliability in complex and harsh environments, and minimize environmental impact and health risks. This study explores the influence of two different formulations of low viscosity lubricants, tested through actual road endurance trials, on a hybrid vehicle’s aftertreatment system performance and overall emission levels. The study includes 120,000 km of endurance testing in four different challenging environments in China, as well as 90,000 km of endurance testing in a typical urban and highway driving cycle in a large city. Results indicate that emissions from the test vehicles during the 120,000 km and 210,000 km durable Worldwide harmonized Light vehicle Test Cycles (WLTCs) meet China’s Stage 6 light-duty vehicle emission standards, with the 210,000 km Real Driving Emission test (RDE) results also conforming to these standards. Relative to fresh TWC, the light-off temperature increased by a mere 60 °C, and the oxygen storage capacity declined by around 19% following endurance testing. Additionally, the GPF exhibited satisfactory performance after 210,000 km of endurance testing, showing lower backpressure values compared to the fresh-coated samples, with no notable ash buildup observed in the substrate. Drawing on the outcomes of actual road endurance testing, this study illustrates that employing low-to-mid-ash-content, low-viscosity lubricants is both compatible and reliable for aftertreatment systems in present or advanced hybrid technologies. Premium lubricants facilitate vehicles in sustaining compliant and stable emission performance, even amid harsh environments and complex operating conditions. Furthermore, the tested lubricants effectively inhibit excessive aging of the aftertreatment system over prolonged mileage. Moreover, this study discusses the feasibility of rapid aging evaluation methods for aftertreatment systems based on engine test benches, juxtaposed with actual road endurance testing. These findings and conclusions offer crucial references and guidance for enhancing lubricant performance and sustainability. Subsequent studies can delve deeper into the correlation between lubricant performance and environmental impact, alongside optimization strategies for lubricants across various vehicle models and usage scenarios.

We discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry is associated with a topological defect and a conserved operator, and the latter can be presented as a matrix product operator. Importantly, unlike its continuum counterpart, the symmetry algebra involves lattice translations. Consequently, it is not described by a fusion category. In the presence of this defect, the symmetry algebra involving parity/time-reversal is realized projectively, which is reminiscent of an anomaly. Different Hamiltonians with the same lattice non-invertible symmetry can flow in their continuum limits to infinitely many different fusion categories (with different Frobenius-Schur indicators), including, as a special case, the Ising CFT. The non-invertible symmetry leads to a constraint similar to that of Lieb-Schultz-Mattis, implying that the system cannot have a unique gapped ground state. It is either in a gapless phase or in a gapped phase with three (or a multiple of three) ground states, associated with the spontaneous breaking of the lattice non-invertible symmetry.

We study the symmetries of closed Majorana chains in 1+1d, including the translation, fermion parity, spatial parity, and time-reversal symmetries. The algebra of the symmetry operators is realized projectively on the Hilbert space, signaling anomalies on the lattice, and constraining the long-distance behavior. In the special case of the free Hamiltonian (and small deformations thereof), the continuum limit is the 1+1d free Majorana CFT. Its continuum chiral fermion parity $(-1)^{F_\text{L}}$ emanates from the lattice translation symmetry. We find a lattice precursor of its mod 8 't Hooft anomaly. Using a Jordan-Wigner transformation, we sum over the spin structures of the lattice model (a procedure known as the GSO projection), while carefully tracking the global symmetries. In the resulting bosonic model of Ising spins, the Majorana translation operator leads to a non-invertible lattice translation symmetry at the critical point. The non-invertible Kramers-Wannier duality operator of the continuum Ising CFT emanates from this non-invertible lattice translation of the transverse-field Ising model.