Carbonate reservoirs, characterized by extensive fractures and cavities, are prone to gravity displacement during drilling when the bottom-hole pressure approaches equilibrium. This phenomenon, driven by density differences between drilling and formation fluids, can result in simultaneous overflow and leakage, posing significant well control risks such as kicks or blowouts. The occurrence of gravity displacement downhole makes its timely detection through conventional annular flow monitoring techniques challenging. This study investigates the triggering conditions and safe density window for gravity displacement in fractured and cavernous formations. Through theoretical analysis and experimental simulation, we examined the displacement mechanisms in both fractured and cavernous conditions. Computational fluid dynamics (CFDs) simulations were used to validate critical fluid column heights for fractured formations and the proposed safe density window. Based on these findings, practical methods to mitigate the hazards associated with gravity displacement overflow are proposed. The results offer valuable guidance for the field identification and mitigation of such incidents, contributing to managed pressure drilling and enhancing drilling safety in complex carbonate reservoirs.

Non-methane hydrocarbons in the earth are predominantly sourced from the thermal degradation of organic matter (thermogenesis). Abiogenic polymerization has been proposed as an alternative mechanism of hydrocarbon creation in Precambrian shields, based on differences in carbon and hydrogen isotopic compositions between co-existing compounds. However, inverse isotopic signatures have been observed in thermogenic systems, suggesting this evidence is ambiguous. Prior work suggested low values of Δ 13 C 2 H 6 (a measure of the departure from stochastic abundances of 13 C 13 CH 6 ) in ethane recovered from Kidd Creek formation waters are consistent with formation via abiotic polymerization (Taguchi et al., 2022). We have developed dual clumped isotopic measurements (Δ 13 C 2 H 6 and Δ 12 C 13 CH 5 D) in ethane to investigate the sources and processes involved in the creation and destruction of terrestrial ethane from petroleum fields, fracture fluids from the Canadian Shield, and other sources. Our results suggest that ethanes created from all studied formation pathways and not subjected to subsequent intense heating are characterized by disequilibrated intermolecular and intramolecular isotope signatures. In low maturity thermogenic gases, both kinetic isotope effects and source inheritance can impart strongly disequilibrated Δ 12 C 13 CH 5 D signatures in product ethane, resulting in at least two distinct and recognizable thermogenic end members. Low Δ 13 C 2 H 6 and Δ 12 C 13 CH 5 D signatures at Kidd Creek on the Canadian Shield are distinct from thermogenic ethanes and consistent with radical-mediated polymerization, favoring interpretation of abiotic origins. Δ 12 C 13 CH 5 D values for thermogenic ethanes approach equilibrium with increasing thermal maturity, consistent with suggestions from other intramolecular and intermolecular isotopic signatures in hydrocarbon systems that suggest partial equilibration through ‘metathetic’ chemical cycles (e.g., radical reaction networks) or interaction with solid catalysts.

Whether and how a system approaches equilibrium is a central issue in nonequilibrium statistical physics, underpinning our understanding of both thermalization and heat transport. Bogoliubov's three-stage (initial, kinetic, and hydrodynamic) evolution hypothesis provides a qualitative framework, but quantitative advances have mostly been restricted to near-integrable systems such as dilute gases. In this work, we investigate the relaxation dynamics of a one-dimensional diatomic hard-point gas and present a phase diagram that comprehensively characterizes relaxation behavior across the full parameter space, from near-integrable to far-from-integrable regimes. We first analyze thermalization (local energy relaxation in nonequilibrium states) and identify three universal dynamical regimes: (1) In the near-integrable regime, kinetic processes dominate (initial <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mo>+</a:mo> </a:math> kinetic phase), local energy relaxation decays exponentially, and the thermalization time <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>τ</b:mi> </b:math> scales with perturbation strength <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>δ</c:mi> </c:math> as <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>τ</d:mi> <d:mo>∝</d:mo> <d:msup> <d:mi>δ</d:mi> <d:mrow> <d:mo>−</d:mo> <d:mn>2</d:mn> </d:mrow> </d:msup> </d:mrow> </d:math> . (2) In the far-from-integrable regime, hydrodynamic effects dominate (initial <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mo>+</e:mo> </e:math> hydrodynamic phase), local energy relaxation follows power-law decay, and thermalization time scales linearly with system size <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>N</f:mi> </f:math> . (3) In the intermediate regime, Bogoliubov phase emerges, marked by the transition from kinetic to hydrodynamic relaxation. The phase diagram further reveals that hydrodynamic behavior can emerge even in small systems when the system is sufficiently far from the integrable regime, challenging the conventional view that such effects are only significant in large systems. In the thermodynamic limit, the system's relaxation behavior depends on the order in which the limits ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>N</g:mi> <g:mo>→</g:mo> <g:mi>∞</g:mi> </g:mrow> </g:math> or <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>δ</h:mi> <h:mo>→</h:mo> <h:mn>0</h:mn> </h:mrow> </h:math> ) are taken. We then turn to heat transport (decay of heat-current fluctuations in equilibrium) and demonstrate that its behavior is fully consistent with the thermalization process, leading to the first unified theoretical description of thermalization and heat transport. Our results establish a comprehensive view of relaxation in classical many-body systems and suggest a route for studying similar dynamics in quantum systems, highlighting universal scaling laws and the interplay of kinetic and hydrodynamic processes across integrability regimes.

IntroductionHeat stroke can rapidly progress to end organ damage and death if not promptly treated. The diagnosis is characterized by core body temperature > 40.5 °C. In this study we evaluate how the form of ice (crushed vs cubed), the addition of sodium chloride, and the initial temperature of water together affect the rate of cooling for standardized cooling bath mixtures used to treat patients experiencing heat stroke.MethodsWe prepared four cold water immersion mixtures using 12 quarts of ice and 12 quarts of water (11.36 liters) under different conditions:Test Case 1: Cubed ice with trauma bay tap water (~35 °C);Test Case 2: Crushed ice with cold tap water (~24 °C);Test Case 3: Crushed ice with cold tap water plus four pounds of rock salt;Test Case 4: Cubed ice with cold tap water,After each mixture was poured into a 40-quart bucket and mixed thoroughly, we recorded the temperature at 20-second intervals over a total duration of 300 seconds using a food-grade thermometer. Room temperature during the experiment was 25.0 °C.ResultsAfter 100 seconds, water from the trauma bay with cubed ice reached 6.2 °C, while cold tap water with cubed ice cooled to a slightly lower temperature of 5.5 °C. Crushed ice in cold tap water reached an even lower temperature of 3.6 °C. The coldest mixture was made with crushed ice with salt, which rapidly reduced the water temperature to 2.2 °C. It took approximately 300 seconds for all test groups to approach equilibrium, with final temperatures of 2.4. °C for cubed ice in trauma bay water, 1.4 °C for cubed ice in cold tap water, 1.2 °C for crushed ice in cold tap water, and 0.2 °C for crushed ice with salt in cold tap water.ConclusionA mixture of cold tap water, crushed ice, and sodium chloride achieved a lower equilibrium temperature and cooled more rapidly than mixtures lacking salt, using cubed ice, or prepared with warmer initial water temperature. These findings suggest that optimizing cold water immersion protocols with crushed ice, added salt, and the coolest available tap water may enhance cooling speed in simulated mixtures. Whether these differences translate into improved patient outcomes remains to be determined.

Comprehensive research on phase behavior during the staged conversion of producing oil reservoirs into underground natural gas storage remains limited, particularly under cyclic injection-withdrawal conditions where interphase mass transfer continuously evolves. In this study, we performed high-pressure/high-temperature (HP/HT) visualization experiments using a multistage protocol that mimics reservoir-to-UGS conversion, including primary depletion followed by six rolling cycles of gas injection-withdrawal (upper pressure fixed at 29 MPa; lower pressure stepwise decreased to 10 MPa). To quantify the interphase mechanism in a cycle-resolved manner, we introduced the net mass transfer (NMT) and the net mass transfer rate (NMRT), defined as the net interphase transfer magnitude normalized by the pressure change during each injection or withdrawal step; NMRT > 0 indicates net gas-to-oil transfer dominated by condensation/dissolution, whereas NMRT < 0 indicates net oil-to-gas transfer dominated by vaporization/extraction.The results reveal three distinct stages: (1) Depletion Stage, characterized by oil-phase vaporization and initial gas cap formation, with recovery efficiency controlled by depletion pressure; (2) Rolling Storage Construction (Cycles 1-4), which injection shows positive NMRT (0.115 mL/MPa; condensation/dissolution), lightening the oil and improving the phase envelope, whereas withdrawal shows negative NMRT (-0.357 mL/MPa; vaporization/extraction), enriching C7+ and weakening extraction over cycles;(3) Late-Stage Construction (Cycles 5-6), where condensation/dissolution and vaporization/extraction processes approach equilibrium, with net mass transfer rates nearing zero. After depletion and six rolling cycles, the cumulative oil recovery reached 56.02%, and the available gas storage capacity under standard conditions reached 9.98 × 103 cm3, corresponding to 68.6% of the reactor pore volume. These findings clarify how cycle-wise mass transfer governs phase behavior evolution and provide guidance for optimizing operational parameters during reservoir-to-UGS conversion.

Abstract Reliable estimates of climate sensitivity require understanding how patterns of surface temperature change influence the global radiative feedback. Here we present a theoretical basis for this pattern effect as it relates to the longwave clear sky feedback. A moist adiabatic feedback framework is developed that partitions the feedback into components associated with locally determined moist adiabatic processes and components associated with deviations therefrom, such as due to nonlocal influences and relative humidity changes. Applying this feedback framework to simulations forced by transient and equilibrium patterns of sea surface temperature change reveals that the pattern effect is driven by different physical processes in different geographic regions. In the subtropics, the more stabilizing feedback under transient climate change is explained by a more negative relative humidity feedback. Over the Southern Ocean, the less stabilizing feedback under transient climate change occurs due to the muted surface warming there, which promotes a weak surface temperature feedback; furthermore, for an idealized pattern of change in which the transient sea surface temperature change is uniformly increased but retains the same structure, the pattern effect essentially disappears. The moist adiabatic feedback framework demonstrates that the evolving zonal-mean longwave clear sky feedback—towards stabilization at high latitudes and destabilization at low latitudes, as the climate approaches equilibrium—is controlled by processes, specifically surface temperature and relative humidity feedbacks, not isolated by conventional feedback analysis. In the global mean, the destabilization effect proves larger, receiving additional contributions from small but geographically extensive differences in the fixed-relative humidity atmospheric temperature feedback.

In deep mining engineering, high-stress roadways frequently experience severe damage, thereby compromising the stability of the surrounding rock. This study investigates the stress-energy evolution in the 31,402 material roadway in Hongqinghe Coal Mine through numerical simulation and field measurement. The study focuses on three critical stages of its whole life cycle: facing the excavation roadway, gob-side entry driving, and mining of the working face. The mechanical behavior of each stage shows significant differences. The results show that while facing the excavation roadway, the primary areas of stress concentration and energy dissipation were observed to be approximately 4m from the goaf driving heading. As the gob-side entry progresses, the stress distribution within the coal pillar transitions to a bimodal pattern, with most energy dissipation occurring on the gob side. When mining the 31,402 working face, the stress distribution across the coal pillar approaches equilibrium, and the energy dissipation pattern evolves into a bimodal form. A partition control strategy for different stages of roadway surrounding rock is proposed, and the support parameters are determined. Engineering practice demonstrates that this technology can effectively control the deformation of the surrounding rock in roadways.

Using Excel and its Solver feature, a novel method of analyzing the component reactions of an overall reaction is outlined. As an example, autothermal reforming (300–700 °C) of acetic acid (AA), a significant component of pyrolysis oil, was considered. The overall reaction can be viewed as comprising five individual reactions: reforming, oxidation, water–gas shift, reverse Boudouard, and methanation. A laboratory apparatus was set up in which acetic acid, air, and water were continuously fed to a BASF dual-layer catalytic reactor in plug flow at 1 atm. For this setup, it is easy to construct a material balance in Excel in which five factors, fi, are defined which represent the fraction of reactant going to each of the individual five reactions. Using the Solver feature of Excel, it can readily be determined which of the five factors fi produce the best match of the calculated exit gas composition with the measured gas concentrations for CO, CO2, H2, CH4, and O2. Furthermore, a program such as GasEq or Aspen can then be used to calculate the theoretical equilibrium gas composition at a given condition. Using this equilibrium gas composition and Solver, the individual (fi)equilb can be calculated. Thus, the ratio fi/(fi)equilb is an indication of how close each component reaction is to equilibrium. In this way, an idea is gained of which of the individual component reactions need to be improved or inhibited or if operating parameters should be adjusted. For the specific case of autothermal reforming of acetic acid, the steam reforming reaction requires at least 600 °C to approach equilibrium. In contrast, the oxidation reaction goes to equilibrium throughout the temperature range, completely consuming oxygen. The water–gas shift reaction appears to approach equilibrium to the extent of 71–90% throughout the temperature range. The reverse Boudouard reaction is favored at lower temperatures; in fact, coking was predicted and found at the low temperature of 300 °C.

Abstract The evolution of the spatial pattern of ocean surface warming affects global radiative feedback, yet different climate models provide varying estimates of future patterns. Paleoclimate data, especially from past warm periods, can help constrain future equilibrium warming patterns. By analyzing marine temperature records spanning the past 10 million years with a regression‐based technique that removes temporal dimensions, we extract long‐term ocean warming patterns and quantify relative sea surface temperature changes across the global ocean. This analysis revealed a distinct pattern of amplified warming that aligns with equilibrated model simulations under high CO 2 conditions, yet differs from the transient warming pattern observed over the past 160 years. This paleodata‐model comparison allows us to identify models that better capture fundamental aspects of Earth's warming response, while suggesting how ocean heat uptake and circulation changes modify the development of warming patterns over time. By combining this paleo‐ocean warming pattern with equilibrated model simulations, we characterized the likely evolution of global ocean warming as the climate system approaches equilibrium.

Deformation, chemical reactions, and fluid flow in geological formations are coupled processes. Recent experimental and observational studies suggest that mineral replacement is typically driven by coupled dissolution–precipitation processes, often leading to variable changes in porosity and solid volume depending on the specific reaction conditions. This article builds upon our previous micromechanical model for mineral replacement reactions and the associated deformation processes. Our new model accommodates externally applied stresses and stresses generated as a result of chemical reactions through elastic, viscous, and plastic deformation mechanisms. Our model predicts changes in both porosity and solid volume as a result of the chemical reaction, with these changes governed by the relative rates of deformation of the solid and pore volumes. Porosity reduction often limits the extent of the reaction, while solid volume increase, accompanied by a lesser reduction in porosity, facilitates achieving complete reactions. An interesting finding of our model is the emergence of two solid bulk moduli, typically associated with the presence of a non-connected pore space. However, in our case, they are associated with chemical alterations. We also introduce an effective stress law for reactive porous rocks. We use a two-phase continuum medium approach and local equilibrium thermodynamic models to investigate the coupling between reaction, deformation, and fluid flow on a larger scale. This framework offers valuable insights into the complex interplay between geological processes and the mechanical behavior of rocks undergoing mineral replacement reactions, with implications for understanding subsurface fluid flow and the evolution of geological formations.

Theories of adaptive radiation propose predictable trajectories in which diversity accumulates rapidly in newly formed or colonized environments with underexploited niche space and few competing species, before slowing down as competition intensifies, and speciation and extinction rates approach equilibrium. This historical perspective on diversity may be more important than current environmental variation for explaining today's biodiversity, but this has been difficult to determine because of the complexity of diversification dynamics and the challenges of relating diversification processes to past environmental change. Here we unravel the complex and heterogenous diversification dynamics of Proteaceae (subfamily Grevilleoideae), a large Gondwanan plant clade, to investigate how the expansion and contraction of biomes since the Cretaceous has shaped its current megadiversity across the Sahul region (Australia and New Guinea). We modeled paleobiome dynamics over a 120 Ma period and produced a nuclear phylogenomic dataset of 458 loci for ~700 species (~74%) to show that historical diversification rates across the Grevilleoideae phylogeny are closely associated with ecological opportunity provided by emerging and expanding biomes. Diversification is rapid in emerging and expanding biomes, while long-occupied biomes tend to have higher species richness but lower diversification rates, as expected if these biomes have approached equilibrium diversity. Our results reveal a strong and heterogeneous legacy of climatic and geological history on today's floristic diversity and explain why diversity is often decoupled from expectations based on measures of ecological "carrying capacity" such as the area or climate of present-day biomes.

In this work, we propose a two-parameter parametrization for the deceleration parameter q ( z ) grounded in thermodynamic constraints and applied it to explore the evolution of the universe. The second law of thermodynamics imposes essential conditions to ensure that the system approaches equilibrium in late times, requiring q ( z ) ≥ − 1 and d q d z > 0 as z → − 1 . These constraints ensure that entropy does not decrease, stabilize the system, and facilitate a smooth transition from deceleration to acceleration, consistent with the observed cosmic expansion. Furthermore, the model avoids the phantom regime ( ω < − 1 ), preventing catastrophic future scenarios such as the Big Rip. Using the combined CC, Pantheon, SH0ES, and BAO datasets, we constrain the model parameters and compare the results with the standard ΛCDM model. Our findings indicate H 0 = 70.82 ± 0.88 , with a transition redshift of z t = 0.597 ± 0.214 , suggesting an earlier onset of acceleration compared to ΛCDM. The present deceleration parameter, q 0 = − 0.364 ± 0.032 , implies a weaker acceleration than in ΛCDM. Moreover, we analyze the evolution of total energy density, pressure, and the effective equation of state parameter, confirming a quintessence-like behavior with ω 0 = − 0.570 ± 0.056 . Our results provide a thermodynamically consistent framework for cosmic expansion, supporting a dark-energy-driven acceleration.

Methane is a major greenhouse gas and a key component of global biogeochemical cycles. Microbial methane often deviates from isotope and isotopolog equilibrium in surface environments but approaches equilibrium in deep subsurface sediments. The origin of this near-equilibrium isotopic signature in methane, whether directly produced by methanogens or achieved through anaerobic oxidation of methane (AOM), remains uncertain. Here, we show that, in the absence of AOM, microbial methane produced from deep-sea sediments exhibits isotopolog compositions approaching thermodynamic equilibrium due to energy limitation. In contrast, microbial methane from salt marsh and thermokarst lakes exhibits significant hydrogen and clumped isotopic disequilibrium due to high free-energy availability. We propose that clumped isotopologs of methane provide a proxy for characterizing the bioenergetics of environments for methane production. Together, these observations demonstrate methane clumped isotopes as a powerful tool to better understand the relation between methane metabolisms and the energy landscape in natural environments.

The out-of-time-ordered correlator (OTOC) is a popular probe for quantum information spreading and thermalization. In systems with local interactions, the OTOC defines a characteristic butterfly light cone that separates a regime unperturbed by chaos from one where time-evolved operators and the OTOC approach equilibrium. This relaxation has been shown to proceed in two stages. The first stage exhibits an extensive timescale and a decay rate known as the “phantom eigenvalue”, which is slower than the gap of the transfer matrix. In this paper, we investigate the two-stage relaxation of the OTOC towards its equilibrium value in various local quantum circuits. We apply a systematic framework based on an emergent statistical model, where the dynamics of two single-particle modes—a domain wall and a magnon—govern the decay rates. We show that a configuration with coexisting domain wall and magnon modes generates the phantom rate in the first stage, while competition between these two modes determines the second stage. We also examine this relaxation within the operator cluster picture. The magnon modes translate into a bound state of clusters, and the domain wall into a random operator, giving consistent rates. Finally, we extend our findings from random-in-time circuits to a broad class of Floquet models.

The oxygen isotope composition of seawater (δ18Oseawater) is shaped by high- and low-temperature rock-water interactions, reflecting Earth system’s dynamics and evolution. The history of δ18Oseawater remains debated due partly to post-depositional imprints to all current mineral proxies. The oxygen atoms in sulfate minerals are among the most inaccessible to later exchange but often not in isotope equilibrium with ambient water. However, the δ18Osulfate may reach a plateau or approach equilibrium with the δ18Oseawater as the corresponding δ34Ssulfate increases during microbial sulfate reduction. Here we show 289 paired δ18O-δ34S values for sedimentary barite spanning six periods of the Phanerozoic Eon. The δ18O-δ34S trajectories point to variable equilibrium δ18Obarite values for different periods. A ~ 4‰ lower δ18Oseawater value is evident before the Carboniferous than today if assuming the same formation temperature. Utilizing the barite δ18O-δ34S trajectory approach, we now have a robust proxy to advance the long-debated issue of seawater δ18O history.

The esterification of 2,5-furandicarboxylic acid (FDCA) and ethylene glycol (EG) constitutes a critical initial step in the synthesis of poly(ethylene-2,5-furandicarboxylate) (PEF), a promising biobased alternative to the conventional petroleum-based polyethylene terephthalate with superior physiochemical properties. This work presented experimental and kinetic modeling studies on FDCA-EG esterification for the synthesis of PEF using tetrabutyl titanate as a catalyst at 190–220 °C. A reaction network was proposed, incorporating the reversible esterification, transesterification, and, particularly, the decarboxylation of terminal carboxyl groups to elucidate the coloration phenomenon in PEF synthesis. A comprehensive kinetic model, integrating the reaction kinetics and water removal, was developed using the terminal group method from the homogeneous-stage experiments and validated by the reactions in the heterogeneous stage. The model enables accurate prediction of the time to reach a clear point, the esterification rate, and the concentrations and selectivities of key terminal groups and components under varying conditions. Model implication reveals temperature and water removal efficiency (kLa) as dominant kinetic drivers, while equilibrium water concentration governs the minimum level of terminal carboxyl groups and equilibrium esterification rates, which remain unaffected by temperature or kLa. Although all three parameters show negligible effects on ester product selectivity, byproduct selectivity becomes sensitive to these parameters as the system approaches equilibrium, emphasizing the need to avoid equilibrium extremes for decarboxylation mitigation. These insights provide a kinetic framework to balance reaction regulation and byproduct mitigation, enabling optimized FDCA-EG esterification and efficient PEF synthesis through appropriate process intensification.

We quantify the effects of intensely applied electric fields on the Fe oxidation mechanism. The specimen are pristine Fe single crystals exposing a variety of surface structures identified by field ion microscopy. These crystals are simultaneously exposed to low pressures of pure oxygen gas, on the order of 10-7 mbar, while applying intense electric fields on their surface of several tens of volts per nanometer. The local composition of the different surface structures is probed directly and in real time using an Environmental Atom Probe and successfully compared with first principles-based models. We found that rough Fe{244} and Fe{112} facets are more reactive toward oxygen than compact Fe{024} and Fe{011} facets. Results demonstrate that the influence of an electric field on the oxidation kinetics depends on the timescales that are involved as the system evolves toward equilibrium. The initial oxidation kinetics show that strong increases in electric fields facilitate the formation of an oxide. However, as one approaches equilibrium, high field values mitigate this formation. Ultimately, this study elucidates how high externally applied electric fields can be used to dynamically exploit reaction dynamics at the nanoscale towards desired products in a catalytic reaction at mild reaction conditions.

Abstract We quantify the effects of intensely applied electric fields on the Fe oxidation mechanism. The specimen are pristine Fe single crystals exposing a variety of surface structures identified by field ion microscopy. These crystals are simultaneously exposed to low pressures of pure oxygen gas, on the order of 10−7 mbar, while applying intense electric fields on their surface of several tens of volts per nanometer. The local composition of the different surface structures is probed directly and in real time using an Environmental Atom Probe and successfully compared with first principles‐based models. We found that rough Fe{244} and Fe{112} facets are more reactive toward oxygen than compact Fe{024} and Fe{011} facets. Results demonstrate that the influence of an electric field on the oxidation kinetics depends on the timescales that are involved as the system evolves toward equilibrium. The initial oxidation kinetics show that strong increases in electric fields facilitate the formation of an oxide. However, as one approaches equilibrium, high field values mitigate this formation. Ultimately, this study elucidates how high externally applied electric fields can be used to dynamically exploit reaction dynamics at the nanoscale towards desired products in a catalytic reaction at mild reaction conditions.

We employ the Full Relativistic Boltzmann Transport approach for a conformal system in 3+1D to study the universal behaviour in moments of the distribution function and anisotropic flows. We investigate different transverse system sizes R and interaction strength η/s and identify universality classes based upon the interplay between R and the mean free path; we show that each of this classes can be identified by a particular value of the opacity γ^, which has been previously introduced in literature. Our results highlight that, at early times, the inverse Reynolds number and momentum moments of the distribution function display universal behaviour, converging to a 1D attractor driven by longitudinal expansion. This indicates that systems of different sizes and interaction strengths tend to approach equilibrium in a similar manner. We provide a detailed analysis of how the onset of transverse flow affects these moments at later times. Moreover, we investigate the system size and η/s dependence for the harmonic flows v2,v3,v4 and their response functions, along with the impact of the η/s and the system transverse size on the dissipation of initial azimuthal correlations in momentum space. Finally, we introduce the normalised elliptic flow v2/v2,eq, showing the emergence of attractor behaviour in the regime of large opacity. These results offer new insights into how different systems evolve towards equilibrium and the role that system size and interaction play in this process.

Covalent organic frameworks (COFs) enable the precise and controlled synthesis of single-atom catalysts with uniformly distributed active metal centers, offering opportunities to elucidate the impact of subtle coordination environment changes on the catalytic performance. Inspired by N-confused porphyrins, we designed 20 metalloporphyrin-based COFs with either M-N3C1 or M-N4 centers, where M refers to 3d transition metals from Sc to Zn, for the electrocatalysis of oxygen reduction reaction (ORR). Density functional theory calculations predicted Co-based COFs to be the best ORR catalysts among the screened catalysts. Hence, Co-N3C1-COF and Co-N4-COF with a high crystallinity were synthesized. The Co-N3C1-COF exhibited improved ORR performance over the parent Co-N4-COF, as it had a reduced overpotential and increased four-electron selectivity, corroborating theoretical predictions. The enhanced performance was ascribed to the increase in electron density on Co as the coordination environment transits from Co-N4 to Co-N3C1. This not only facilitated the adsorption of O2 and critical intermediates but also changed the potential-determining step, which in turn made the ORR free energy profile of Co-N3C1-COF approach equilibrium for all elementary steps, thus leading to a reduced overpotential. This combined theoretical and experimental work exemplified carbon coordination in porphyrin-based COFs as an effective strategy to facilitate the catalytic capability for ORR. A descriptor was also provided to guide the design of coordination-varied Por-COFs catalysts.