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Lithium‐sulfur (Li‐S) batteries hold immense promise as next‐generation energy storage due to their high theoretical energy density (2600 Wh kg⁻¹), low cost, and non‐toxic nature. However, practical implementation faces challenges, primarily from Li polysulfide (LiPS) shuttling within the cathode and Li dendrite growth at the anode. Optimized electrodes/electrolytes design effectively confines LiPS to the cathode, boosting cycling performance in coin cells to up to hundreds of cycles. Scaling up to larger pouch cells presents new obstacles, requiring further research for long‐term stability. A 1.45 Ah pouch cell, with optimized sulfur loading and electrolyte/sulfur ratio is developed, which delivers an energy density of 151 Wh kg⁻¹with 70% capacity retention up to 100 cycles. Targeting higher energy density (180 Wh kg⁻¹), the developed 1Ah pouch cell exhibits 68% capacity retention after 50 cycles. Morphological analysis reveals that pouch cell failure is primarily from Li metal powdering and resulting polarization, rather than LiPS shuttling. This occurs for continuous Li ion stripping/plating during cycling, leading to dendrite growth and formation of non‐reactive Li powder, especially under high currents. These issues increase ion diffusion resistance and reduce coulombic efficiency over time. Therefore, the study highlights the importance of a protected Li metal anode for achieving high‐energy‐dense batteries.

 

Given a graph sequence and a simple connected subgraph , we denote by the number of monochromatic copies of in a uniformly random vertex coloring of with colors. We prove a central limit theorem for (we denote the appropriately centered and rescaled statistic as ) with explicit error rates. The error rates arise from graph counts of collections formed by joining copies of which we callgood joins. Good joins are closely related to the fourth moment of , which allows us to show afourth moment phenomenonfor the central limit theorem. For , we show that converges in distribution to whenever its fourth moment converges to 3. We show the convergence of the fourth moment is necessary to obtain a normal limit when .

 

We introduce Poisson boundaries of II $_1$ factors with respect to density operators that give the traces. The Poisson boundary is a von Neumann algebra that contains the II $_1$ factor and is a particular example of the boundary of a unital completely positive map as introduced by Izumi. Studying the inclusion of the II $_1$ factor into its boundary, we develop a number of notions, such as double ergodicity and entropy, that can be seen as natural analogues of results regarding the Poisson boundaries introduced by Furstenberg. We use the techniques developed to answer a problem of Popa by showing that all finite factors satisfy his MV property. We also extend a result of Nevo by showing that property (T) factors give rise to an entropy gap.