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DOE OSTI2024

Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools.

Eigenstate thermalization↗

DOE OSTI2021

HFTS-2 Completions Design and State-of-the-Art Diagnostics Results

Various completion schemes were tested as part of the Hydraulic Fracture Test Site-2 (HFTS-2) project. The wells were instrumented with permanent fiber optic (FO) cable, and unique near-wellbore and far-field region surveys were acquired to evaluate spatial and temporal hydraulic fracture characteristics. The state-of-the-art diagnostics included substantial monitoring of both the well stimulation and longer-term production performance. The objective was to evaluate and improve stimulation distribution effectiveness (SDE) for different completion designs based on the diagnostics results. A hydraulic fracturing (HF) profile (i.e., proppant/fluid allocation among clusters) was obtained using near-wellbore Distributed Acoustic Sensing (DAS) data acquired during stimulation. Statistical analysis provided a quantitative assessment of SDE for the different completion designs. A novel workflow was developed to assess time-lapse fracture property changes at the cluster and stage levels based on Distributed Strain Sensing (DSS) data acquired during the production phase. These time-lapse fracture property changes were compared with the HF profile. Based on the statistical analysis, Rate Per Cluster (RPC) during proppant slurry placement appears to be a primary completion design variable, rather than the typical Rate Per Perf (RPP). If RPC was not maintained at a certain level, the likelihood of uneven distribution increased dramatically. The stage configurations that created low RPC while maintaining high RPP did not show improved SDE. The strain change results based on DSS data during the production phase indicated near-wellbore fracture property changes (e.g., aperture changes during well shut-in and flow periods) and aligned well with near-wellbore DAS signals acquired during stimulation. More importantly, fracture property changes based on DSS data acquired during two tests over a 7-month period show high consistency and good alignment with the near-wellbore HF profile. This workflow quantitatively evaluates SDE for different completion designs using diagnostic results and could help optimize completion strategy for future development projects. Here, the analysis and interpretation of results demonstrate the technical feasibility of using permanent fiber optic cable for stimulation and production monitoring and indic

58 GEOSCIENCES↗

DOE OSTI2026

Bioenergy Cropping Reduces the Spatiotemporal Scaling of Soil Bacterial Biodiversity

Widespread bioenergy cropping can transform landscapes, strongly affecting biodiversity. However, the impact of bioenergy cropping on the spatiotemporal scaling of soil biodiversity remains virtually unknown, despite its profound implications for the functioning of the ecological community. Here, we investigated how bioenergy cropping influenced the spatiotemporal scaling of soil bacterial biodiversity in marginal soils (sandy loam and clay loam soils) in Oklahoma, USA. We detected strong, significant species-time-area relationships (STARs) and phylogenetic-time-area relationships (PTARs) in bacterial communities and their lineages, suggesting that STARs and PTARs exist in microbial ecology within the studied system. Also, spatiotemporal scaling rates (the slopes of STAR and PTAR models) varied substantially among bacterial lineages and were positively correlated with their 16S rRNA gene copy numbers, a genomic trait indicative of microbial growth potentials. Strikingly, bioenergy cropping significantly reduced spatiotemporal scaling rates by 6.8%-14.1%, with a more pronounced reduction observed in sandy loam soils, where those rates were significantly lower than in clay loam soils. The heterogeneity of soil phosphorus and carbon resulted in variations in bacterial spatiotemporal scaling rates. Collectively, our findings suggest that bioenergy cropping may alleviate rapid shifts in soil biodiversity across space and time, thereby stabilizing soil biodiversity and supporting its role as part of sustainable land management and climate mitigation strategies.

bacterial diversity↗