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It has been argued that the entanglement spectrum of a static patch of de Sitter space must be flat, or what is equivalent, the temperature parameter in the Boltzmann distribution must be infinite. This seems absurd: quantum fields in de Sitter space have thermal behavior with a finite temperature proportional to the inverse radius of the horizon. The resolution of this puzzle is that the behavior of some quantum systems can be characterized by a temperature-like quantity which remains finite as the temperature goes to infinity. For want of a better term we have called this quantity tomperature. In this paper we will explain how tomperature resolves the puzzle in a proposed toy model of de Sitter holography -- the double-scaled limit of SYK theory.

Post-Wilsonian physics views theories not as isolated points but elements of bigger universality classes, with effective theories emerging in the infrared. This paper makes initial attempts to apply this viewpoint to homogeneous geometries on group manifolds, and complexity geometry in particular. We observe that many homogeneous metrics on low-dimensional Lie groups have markedly different short-distance properties, but nearly identical distance functions at longer distances. Using Nielsen's framework of complexity geometry, we argue for the existence of a large universality class of definitions of quantum complexity, each linearly related to the other, a much finer-grained equivalence than typically considered in complexity theory. We conjecture that at larger complexities, a new effective metric emerges that describes a broad class of complexity geometries, insensitive to various choices of 'ultraviolet' penalty factors. Finally we lay out a broader mathematical program of classifying the effective geometries of right-invariant group manifolds.

Massive gully land consolidation projects, launched in China’s Loess Plateau, aim to restore 2667$$\mathrm{km}^2$$${\mathrm{km}}^2$agricultural lands in total by consolidating 2026 highly eroded gullies. This effort represents a social engineering project where the economic development and livelihood of the farming families are closely tied to the ability of these emergent landscapes to provide agricultural services. Whether these ‘time zero’ landscapes have the resilience to provide a sustainable soil condition such as soil organic carbon (SOC) content remains unknown. By studying two watersheds, one of which is a control site, we show that the consolidated gully serves as an enhanced carbon sink, where the magnitude of SOC increase rate (1.0$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$$gC/m^2/\mathrm{year}$) is about twice that of the SOC decrease rate (− 0.5$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$$gC/m^2/\mathrm{year}$) in the surrounding natural watershed. Over a 50-year co-evolution of landscape and SOC turnover, we find that the dominant mechanisms that determine the carbon cycling are different between the consolidated gully and natural watersheds. In natural watersheds, the flux of SOC transformation is mainly driven by the flux of SOC transport; but in the consolidated gully, the transport has little impact on the transformation. Furthermore, we find that extending the surface carbon residence time has the potential to efficiently enhance carbon sequestrationmore »from the atmosphere with a rate as high as 8$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$$gC/m^2/\mathrm{year}$compared to the current 0.4$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$$gC/m^2/\mathrm{year}$. The success for the completion of all gully consolidation would lead to as high as 26.67$$\mathrm{Gg\,C}/\mathrm{year}$$$\mathrm{Gg}C/\mathrm{year}$sequestrated into soils. This work, therefore, not only provides an assessment and guidance of the long-term sustainability of the ‘time zero’ landscapes but also a solution for sequestration$$\hbox {CO}_2$$${\text{CO}}_2$into soils.

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