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Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant behavior as the impact of soil diffusion diminishes compared to fluvial erosion at the landscape scale, yielding complete self-similarity with respect to a dimensionless channelization index. Approaching its zero limit, soil diffusion becomes confined to a region of vanishing area and large concavity or convexity, corresponding to the locus of the ridge and valley network. We demonstrate these results using one dimensional analytical solutions and two dimensional numerical simulations, supported by real-world topographic observations. Our findings on the landscape self-similarity and the localized diffusion resemble the self-similarity of turbulent flows and the role of viscous dissipation. Topographic singularities in the vanishing diffusion limit are suggestive of shock waves and singularities observed in nonlinear complex systems. 

Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker–Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics. 

Abstract Plants with crassulacean acid metabolism (CAM) are increasing in distribution and abundance in drylands worldwide, but the underlying drivers remain unknown. We investigate the impacts of extreme drought and CO₂enrichment on the competitive relationships between seedlings ofCylindropuntia imbricata(CAM species) andBouteloua eriopoda(C₄grass), which coexist in semiarid ecosystems across the Southwestern United States. Our experiments under altered water and CO₂water conditions show thatC. imbricatapositively responded to CO₂enrichment under extreme drought conditions, whileB. eriopodadeclined from drought stress and did not recover after the drought ended. Conversely, in well‐watered conditionsB. eriopodahad a strong competitive advantage onC. imbricatasuch that the photosynthetic rate and biomass (per individual) ofC. imbricatagrown withB. eriopodawere lower relative to when growing alone. A meta‐analysis examining multiple plant families across global drylands shows a positive response of CAM photosynthesis and productivity to CO₂enrichment. Collectively, our results suggest that under drought and elevated CO₂concentrations, projected with climate change, the competitive advantage of plant functional groups may shift and the dominance of CAM plants may increase in semiarid ecosystems.