Type III1 Research Articles

Algebraic ER=EPR and complexity transfer

We propose an algebraic definition of ER=EPR in the GN → 0 limit, which associates bulk spacetime connectivity/disconnectivity to the operator algebraic structure of a quantum gravity system. The new formulation not only includes information on the amount of entanglement, but also more importantly the structure of entanglement. We give an independent definition of a quantum wormhole as part of the proposal. This algebraic version of ER=EPR sheds light on a recent puzzle regarding spacetime disconnectivity in holographic systems with O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(1/GN) entanglement. We discuss the emergence of quantum connectivity in the context of black hole evaporation and further argue that at the Page time, the black hole-radiation system undergoes a transition involving the transfer of an emergent type III1 subalgebra of high complexity operators from the black hole to radiation. We argue this is a general phenomenon that occurs whenever there is an exchange of dominance between two competing quantum extremal surfaces.

Paleoenvironmental reconstruction and organic matter accumulation of the paleogene shahejie oil shale in the Zhanhua Sag, Bohai Bay Basin, Eastern China

The controlling factors of organic-rich shale accumulation is essential for the exploration and development of shale oil and gas resources. The sedimentary environment plays a vital role in the formation of organic-rich sediments in lacustrine facies. This article unravels the mineralogy, geochemistry, and paleoenvironmental evolution during the deposition of the Paleogene Shahejie Formation (Es3L). It discusses the effects of paleoclimate, paleosalinity, paleoredox conditions, paleowater depth, and paleoproductivity on organic matter (OM) enrichment. Finally, the OM enrichment model was established. The results show that the mineralogical compositions are mainly composed of calcite (avg. 40.13%), quartz (avg. 21.64%) and clay minerals (avg. 24.07%), accompanied by dolomite (avg. 7.07%), feldspar (avg. 6.36%) and pyrite (avg. 2.95%). The Es3L shale has a high abundance of OM, with total organic carbon (TOC) ranging from 1.07% to 5.12%. The organic matter type is mainly composed of type Ⅰ-Ⅱ1 kerogen, which is generally considered a good-quality source rock. The source of OM is a mixture of lower bacteria, algae, and plants. During the early sedimentary period, the paleoclimate was dry and cold, with high salinity, intense reducibility, and relatively low productivity. During the late sedimentary period, the climate became warmer and more humid. As a result, the salinity decreased to a level that was suitable for biological reproduction, and productivity increased gradually due to the input of terrigenous plants. Paleosalinity and paleoclimate determined the environment of the sedimentary period, in addition, paleoproductivity and paleoredox condition indicated the formation and preservation conditions of OM. The warm and humid climate, brackish water, suitable reduction conditions and high productivity are the favorable conditions for the generation and preservation of organic matter. The research results may have implications for the genetic mechanisms of organic matter accumulation. They will provide theoretical and technical insights into the exploration and development of shale oil.

Ergodic states on type III1 factors and ergodic actions

Abstract Since the early days of Tomita–Takesaki theory, it is known that a von Neumann algebra 𝑀 that admits a state 𝜑 with trivial centralizer M φ M_{\varphi} must be a type III1 factor, but the converse remained open. We solve this problem and prove that such ergodic states form a dense G δ G_{\delta} set among all faithful normal states on any III1 factor with separable predual. Through Connes’ Radon–Nikodym cocycle theorem, this problem is related to the existence of ergodic cocycle perturbations for outer group actions, which we consider in the second part of the paper.

Geochemical Characteristics of Mesoproterozoic Source Rocks in North China: Insights for Organic Matter Enrichment and Thermal Evolution

In recent years, the exploration of oil and gas in China’s Precambrian strata has garnered significant attention, leading to notable advancements in exploration play assessment. However, there is a dearth of published literature on Proterozoic source rocks’ organic sources, sedimentary environments, marine hydrochemistry, and other attributes. This study focuses on investigating potential source rocks within the Hongshuizhuang and Xiamaling Formations in the Jibei Depression of North China. A comprehensive analysis was conducted to evaluate hydrocarbon generation characteristics, using hydrocarbon biomarkers and polar compounds as geochemical indicators for precursor biota and maturity levels. The results indicate high organic matter abundance with predominantly type I-II1 organic matter composition in the studied source rocks. These samples are at an immature–low mature stage, with the potential for primarily generating aromatic crude oil. The parent material is mainly attributed to lower aquatic organisms, such as bacteria and algae. The sedimentary environment exhibits marine facies, characterized by high evaporation rates, salinity levels, and strong euxinic conditions, that led to sulfur incorporation into the organic matter matrix. It should be noted that correlations between biomarker parameters and maturity may not be fully applicable to ancient source rocks; however, the methyldibenzothiophene ratio (MDR) demonstrates a strong correlation with Tmax. The compounds and their total monoisotope ions abundance (TMIA) were primarily identified and analyzed using FT–ICR MS. It was observed that these compounds were influenced by the depositional environment and organic matter maturity. Importantly, it was clearly demonstrated that the DBE and carbon number range of CH compounds gradually increased with maturity, due to the removal of N, S, and O functional groups. Specifically, N1 compounds predominantly consisted of carbazoles with short alkyl side chains which readily converted into N1Ox compounds. On the other hand, O1 compounds mainly comprised benzofurans with low abundance, indicating a reducing sedimentary environment, as suggested by their low TMIA values. Furthermore, S1 compounds were primarily thiophenes whose DBE range and carbon number increased with maturity, possibly suggesting an abiotic input of inorganic sulfur. Notably, the maturity indices (MAT) proved suitable for Mesoproterozoic source rocks while exhibiting strong linear relationships.

Information loss, mixing and emergent type III1 factors

A manifestation of the black hole information loss problem is that the two-point function of probe operators in a large Anti-de Sitter black hole decays in time, whereas, on the boundary CFT, it is expected to be an almost periodic function of time. We point out that the decay of the two-point function (clustering in time) holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity.We call operators that cluster in time “mixing” and explore the necessary and sufficient conditions for mixing. The information loss problem is a special case of the statement that in type I algebras, there exists no mixing operators. We prove that, in a thermofield double state (KMS state), if mixing operators form an algebra (close under multiplication), the resulting algebra must be a von Neumann type III1 factor. In other words, the physically intuitive requirement that all nonconserved operators should exponentially mix is so strong that it fixes the observable algebra to be an exotic algebra called a type III1 factor. More generally, for an arbitrary out-of-equilibrium state of a general quantum system (von Neumann algebra), we show that if the set of operators that mix under modular flow forms an algebra, it is a type III1 von Neumann factor.In a theory of Generalized Free Fields (GFF), we show that if the two-point function clusters in time, all operators are mixing, and the algebra is a type III1 factor. For example, in \U0001d4a9 = 4 SYM, above the Hawking-Page phase transition, clustering of the single trace operators implies that the algebra is a type III1 factor, settling a recent conjecture of Leutheusser and Liu. We explicitly construct the C∗-algebra and von Neumann subalgebras of GFF associated with time bands and, more generally, open sets of the bulk spacetime using the HKLL reconstruction map.

Adolescent psychiatry of Y. Kasahara and succeeding research on Hikikomori in Europe and in Japan.

This paper will focus on the works of one of Japan's representative psychiatrists, Yomishi Kasahara, particularly on his works in the 1970s in which he proposed the concept of student apathy, and will discuss how this work was carried over into a contemporary topic, the study of "Hikikomori." Kasahara's well-known paper "Clinical Classification of Depression" (Kasahara and Kimura, 1975) described the present state of patients with Type III as "they do not have a complete set of symptoms as in Type I, but sometimes show dependency, strong exaggeration, complication of other neurotic symptoms, little tendency of self-reproaching, and tendency of accusing others"; the two subtypes as Type III-1 "those that remain at the neurotic level" and Type III-2 "those that transiently drop to the psychotic level." We have summarized and introduced below the case presented in the paper with this Type III-1. From today's perspective, where the concept of "Hikikomori" exists, this case could be considered as a typical case of "Hikikomori," that is, a person with a tendency to avoid social roles and responsibilities and to immerse oneself in areas with no responsibilities, such as hobbies. "Hikikomori" was discovered in the late 1980s, but to be precise, it was just that the concept emerged. The same clinical condition had already been brilliantly found by Kasahara in the 1970s under the concept of "apathy syndrome," which was distinguished from depression.

Algebra of operators in an AdS-Rindler wedge

We discuss the algebra of operators in AdS-Rindler wedge, particularly in AdS5/CFT4. We explicitly construct the algebra at N = ∞ limit and discuss its Type III1 nature. We will consider 1/N corrections to the theory and using a novel way of renormalizing the area of Ryu-Takayanagi surface, describe how several divergences can be renormalized and the algebra becomes Type II∞. This will make it possible to associate a density matrix to any state in the Hilbert space and thus a von Neumann entropy.

Geological characteristics and resources potential of shale oil in Chang 7 Member of Upper Triassic Yanchang Formation in Fuxian area, southern Ordos Basin, western China

Ordos Basin is rich in shale oil resources. Fuxian area in the southern Ordos Basin is an important area where Sinopec is expected to make a breakthrough in the exploration and development of lacustrine shale oil. To further identify the exploration target of shale oil in Chang 7 Member of Fuxian area, Ordos Basin, this study systematically analyzed the sedimentary characteristics, source rock characteristics, reservoir characteristics, oil-bearing characteristics, fracability and preservation conditions of Chang 7 Member in this area. The results show that: (1) the organic matter abundance of shale in the Chang 7 Member is high, and its type is dominated by type I-II1; the maturity is also relatively high, with Ro generally greater than 0.8% in the central and western parts, which is favorable for the generation and accumulation of shale oil. The development of fractures is pretty low, and thus the structure preservation conditions are relatively favorable. Delta front deposits are mainly developed in the northeastern part, while deep lake - semi-deep lake mudstone and gravity-flow deposits are developed in the western part, and the shale oil types are mainly type II and III. (2) Comparing with the western Ordos Basin, the reservoir in Fuxian area has rapid lateral variation and relatively thin cumulative thickness; the thickness of high-quality shale and maturity are low, resulting in low intensity of hydrocarbon generation and low mobility of oil-bearing saturation. Therefore, there is still a need for further improvement and refinement in the exploration evaluation, effective development and engineering techniques. (3) Integrating sedimentary characteristics with shale oil types, source conditions, oil-bearing properties, mobility, fracability and preservation conditions, it is clarified that the Type II shale oil of Chang 72 sub-,Member in Fuxian area is the current realistic exploration type of shale oil, and its favorable target is located in the development area of delta front in the central part and gravity flow in the western part.

Gravity and the crossed product

Recently Leutheusser and Liu [1, 2] identified an emergent algebra of Type III1 in the operator algebra of mathcal{N} = 4 super Yang-Mills theory for large N. Here we describe some 1/N corrections to this picture and show that the emergent Type III1 algebra becomes an algebra of Type II∞. The Type II∞ algebra is the crossed product of the Type III1 algebra by its modular automorphism group. In the context of the emergent Type II∞ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics.

Nonsingular Poisson Suspensions

The classical Poisson functor associates to every infinite measure preserving dynamical system (X, μ, T) a probability preserving dynamical system (X*, μ*, T*) called the Poisson suspension of T. In this paper we generalize this construction: a subgroup Aut2(X, μ) of μ-nonsingular transformations T of X is specified as the largest subgroup for which T* is μ*-nonsingular. The topological structure of this subgroup is studied. We show that a generic element in Aut2(X, μ) is ergodic and of Krieger type III1. Let G be a locally compact Polish group and let A: G → Aut2(X, μ) be a G-action. We investigate dynamical properties of the Poisson suspension A* of A in terms of an affine representation of G associated naturally with A. It is shown that G has property (T), if and only if each nonsingular Poisson G-action admits an absolutely continuous invariant probability. If G does not have property (T), then for each generating probability κ on G and t > 0, a nonsingular Poisson G-action is constructed whose Furstenberg κ-entropy is t.

Quantum error correction in SYK and bulk emergence

We analyze the error correcting properties of the Sachdev-Ye-Kitaev model, with errors that correspond to erasures of subsets of fermions. We study the limit where the number of fermions erased is large but small compared to the total number of fermions. We compute the price of the quantum error correcting code, defined as the number of physical qubits needed to reconstruct whether a given operator has been acted upon the thermal state or not. By thinking about reconstruction via quantum teleportation, we argue for a bound that relates the price to the ordinary operator size in systems that display so-called detailed size winding [1]. We then find that in SYK the price roughly saturates this bound. Computing the price requires computing modular flowed correlators with respect to the density matrix associated to a subset of fermions. We offer an interpretation of these correlators as probing a quantum extremal surface in the AdS dual of SYK. In the large N limit, the operator algebras associated to subsets of fermions in SYK satisfy half-sided modular inclusion, which is indicative of an emergent Type III1 von Neumann algebra. We discuss the relationship between the emergent algebra of half-sided modular inclusions and bulk symmetry generators.

Multi-Type Hydrocarbon Accumulation Mechanism in the Hari Sag, Yingen Ejinaqi Basin, China

With the successful development of unconventional hydrocarbons, the production of unconventional hydrocarbons has increased rapidly. However, a single conventional or unconventional model is not suitable for the mechanism of hydrocarbon accumulation in a given basin or sag. Based on data from drilling, logging, and geophysical analysis, the hydrocarbon accumulation mechanism in the Hari sag in the Yingen-Ejinaqi basin, China, was analyzed. There are three sets of source rocks in the Hari sag: the K1y source rocks were evaluated as having excellent source rock potential with low thermal maturity and kerogen Type I-II1; the K1b2 source rocks were evaluated as having good source rock potential with mature to highly mature stages and kerogen Type II1-II2; and the K1b1 source rocks were evaluated as having moderate source rock potential with mature to highly mature stages and kerogen Type II1-II2. Reservoir types were found to be conventional sand reservoirs, unconventional carbonate-shale reservoirs, and volcanic rock reservoirs. There were two sets of fault-lithologic traps in the Hari sag, which conform to the intra-source continuous hydrocarbon accumulation model and the approaching-source discontinuous hydrocarbon accumulation model. The conclusions of this research provide guidance for exploring multi-type reservoirs and multi-type hydrocarbon accumulation models.

Excellent source rocks found along the margin of a large lacustrine basin: Case study from the Ordos Basin, China

Whether the Chang 6 oil pools of the Triassic Yanchang Formation in the Ansai-Yanchang (AY) oil province on the Yishan slope of the Ordos Basin formed from near source rock or far source rock has long been debated. An understanding of the source rock's position will impact the formation mode and distribution of accumulations in this area. Based on the geochemical data of the Chang 7 source rock in six wells and 18 crude oil samples, the geochemical characteristics of Chang 7 source rock and its relationship with Chang 6 crude oil were studied. There are two types of source rocks, namely, black shales and dark mudstones, present in the AY area. The gross thickness of the Chang 7 black shale is 3.0–19.7 m, with a distribution area of 5500 km2. It has an average total organic carbon (TOC) content of 3.34%, with a chloroform bitumen “A" content of 0.512%, indicating good to excellent source rock potential. The kerogen assessment with core samples shows mixed type I-II1, and has reached peak oil generation, maximum pyrolysis temperatures (Tmax) ranging from 445 to 458 °C. In contrast, the average TOC content of the dark mudstone in Chang 7 is 0.91%, chloroform bitumen “A” is 0.079%, the main type of kerogen is type II2-II1, and Tmax varying from 446 to 461 °C, indicating only fair source rock potential overall. The Chang 7 source rocks in the AY area have a gammacerane index of 0.07–0.38, with an average value of 0.21, which reflects a low-salinity fresh to brackish water environment. The relative abundances of C27, C28, and C29 steranes are 29.7%, 23.1% and 47.2%, respectively, indicating that terrestrial higher plants and aquatic organisms provide similar contribution in the Chang 7 source rocks. Oils produced from the AY area of the Chang 6 member have similar geochemical signatures, but are significantly different from the Chang 6 crude oils in the Daozhen (DZ) area of Ganquan County and the Huaishuzhuang (HSZ) area of Fuxian County, which are located in the center of the lacustrine basin. They differ in terms of the maturity of the oil samples and the microscale composition of the parent material type. The closer the wells are to the center of the lacustrine basin, the higher the maturity of the source rock and the greater the contribution of aquatic organisms. The variation of carbon isotopic composition of Chang 6 crude oil in AY area is consistent with that of Chang 7 shale locally, but opposite to that of Chang 6 crude oil in DZ area. The ratios of nC21-/nC22+, tricyclic terpane/hopane and C29 sterane ββ/(ββ+αα) biomarker parameters of Chang 6 crude oils in AY area are similar to those of Chang 7 shale in local area, but deviate from those of DZ and HSZ area. These data results reveal that the Chang 6 crude oils in the AY oil province are dominated by the local Chang 7 excellent source rocks rather than by the long-distance migration of oils from the basin center.

Characteristics and Controlling Factors of the Chang 8 Oil Reservoir in the Yanchi Area of the Ordos Basin: A Case Study of Well G20

In the Ordos Basin, the Chang 8 oil reservoir of the Triassic Yanchang Formation is the main target of oil exploration and development and there are many factors affecting the hydrocarbon accumulation. Well G20 is an important exploration well in the Yanchi area in the northwestern part of the basin, and the core of the Chang 8 reservoir was sampled and tested to determine the source rocks, trace element composition, mineral composition, reservoir physical properties, and oil-bearing properties. The results show that the rock retrieved exhibits delta plain subfacies; the range of the Chang 8 water body was large, with a gentle slope, and the climate was relatively dry. These findings suggest that this reservoir was deposited in an environment in which sedimentary sand body could easily form. The Chang 8 sandstone reservoir pores are dominated by intergranular pores and feldspar intragranular dissolution pores, indicating that the Chang 8 reservoir is a low-porosity and low-permeability reservoir. Chang 7 source rocks from this area have a type I-II1 hydrocarbon-generating potential, with an average total organic carbon (TOC) content of 5.99% and vitrinite reflectance (Ro) value of 0.48%. Combined with the regional sedimentary evolution, tectonic movement, and reservoir distribution, it is considered that due to the lack of lithologic traps or low-amplitude structural traps, G20 produced water in well testing. The Chang 8 oil reservoir in the Yanchi area can be divided into structural reservoirs and structural-lithologic reservoirs. The conventional oil and gas reservoir exploration ideas of “thick sand belt” and “reservoir sweet spot” are not applicable here. The lithology traps or low-amplitude structural traps and areas with good preservation conditions are the main directions for the next phase of exploration in the northwestern part of the Ordos Basin.

A Comparative Study of Different Quality Oil Shales Developed in the Middle Jurassic Shimengou Formation, Yuqia Area, Northern Qaidam Basin, China

Oil shales are developed in the Shale Member of the Middle Jurassic Shimengou Formation in the Qaidam Basin, China. The oil shales can be classified into three quality groups (low-, medium-, and high-quality oil shales) through a comprehensive analysis protocol that includes Rock-Eval pyrolysis, total organic carbon (TOC) content, proximate analysis, gas chromatography-mass spectrometry (GC-MS), X-ray diffraction (XRD), major and trace element analyses, and maceral analysis. The low-quality oil shales mainly contain type II1 kerogen, the medium-quality oil shales mainly contain type I-II1 kerogen, and the high-quality oil shales mainly contain type I kerogen. All are immature to early thermally mature. The oil yield of the oil shales is directly related to their quality and are positively correlated with TOC content and calorific value. All studied samples were deposited under anaerobic conditions but in different paleoenvironments. The low-quality oil shales were mainly deposited in fresh-water environments, whereas the high-quality oil shales were usually developed in highly saline and reducing environments. Salinity stratification and evidence of algal blooms that are conducive to organic matter enrichment were identified in both medium- and high-quality oil shales, the latter having the highest paleoproductivity and the best preservation conditions. In summary, shale quality is controlled by a combination of factors, including algal abundance, preservation conditions, the existence of algal blooms and salinity stratification, and paleoproductivity. This study reveals how these different factors affect the quality of oil shales, which might provide an in-depth explanation for the formation process of lacustrine oil shales.

Nonsingular Gaussian actions: Beyond the mixing case

Every affine isometric action α of a group G on a real Hilbert space gives rise to a nonsingular action αˆ of G on the associated Gaussian probability space. In the recent paper [2], several results on the ergodicity and Krieger type of these actions were established when the underlying orthogonal representation π of G is mixing. We develop new methods to prove ergodicity when π is only weakly mixing. We determine the type of αˆ in full generality. Using Cantor measures, we give examples of type III1 ergodic Gaussian actions of Z whose underlying representation is non mixing, and even has a Dirichlet measure as spectral type. We also provide very general ergodicity results for Gaussian skew product actions.

Genetic Mechanism and Environment Implications of Siderites in the Lopingian Coal-Bearing Series, Western Guizhou of China: Constrained by Whole-Rock and In Situ Geochemistry

A large number of siderites have been found in the Lopingian (Late Permian) coal-bearing series in western Guizhou, which occurs in various microscopic morphologies and has potential insights into the sedimentary and diagenetic environments. An integrated set of analyses, such as microscopic observation; X-ray diffraction; whole-rock major and trace element, carbon, and oxygen isotope; and in situ major and trace element, has been carried out to unravel the genetic mechanism of the siderites and their environmental implications. According to the microscopic morphology, the siderites can be generally divided into three types and six subtypes, including gelatinous siderites (I), microcrystal-silty siderite [II; microlite siderites (II1), powder crystal siderites (II2)], and spheroidal siderite [III, petal-like siderite (III1), radiating fibrous siderite (III2) and concentric siderite (III3)]. Whole-rock geochemical results show that the iron source for the formation of the siderites was mainly from extensive weathering of the Emeishan high-titanium basalts in hot climate conditions. The carbon and oxygen isotopic results indicate that the origin of CO2 in type I siderites is derived from the dehydroxylation of organic matter. The CO2 in types II1 and II2 siderites is mainly derived from deposited organic matter and marine carbonate rocks, respectively. The CO2 source of type III siderites is sedimentary organic matter and marine carbonate rocks and is affected by different fluids during diagenesis. The whole-rock and in situ geochemical characteristics further point to that type I siderites were formed in the synsedimentary period most strongly affected by seawater. Redox proxies, such as V/Sc, V/(V+Ni), and δ Ce, constrained their formation in a stable and weakly reduced condition. Type II siderites could have been developed in saltwater. Among them, type II1 siderites were formed in the early diagenetic stage, whereas type II2 siderites originated from recrystallization of type II1 siderites and accompanied by metasomatism with calcites under diagenetic fluids of weak reduction to weak oxidation conditions. Type III siderites were formed under the influence of multistage diagenetic fluids. Among them, type III1 siderites formed by the growth of powder crystal siderites (II2) under diagenetic fluids with a weak reducing condition. Type III2 siderites formed by growth around microlite siderites under weak reducing diagenetic fluids. Type III3 siderites formed by concentric growth in diagenetic fluids with weak reduction to weak oxidation conditions and relatively active conditions.

Organic Geochemical Characteristics of Mudstone and Marl from Western Hoh Xil Basin of Tibet

The mudstone and marl from western Hoh Xil basin, located in Tibet of the west of China, were deposited in Tertiary lacustrine environment. Investigation of organic geochemistry, sedimentary characteristics, and 13C in kerogen was conducted to analyze the sedimentary environment, biomarkers, paleoclimate, and source of organic matter during deposition. The Cenozoic sedimentary facies of the basin included upper lacustrine facies and lower alluvial fan facies, which belong to Miocene Wudaoliang Formation and Oligocene Yaxicuo Group, respectively. The Miocene marl-sandstone-mudstone from Wudaoliang Formation was analyzed. Maceral composition was dominated by amorphous organic matter. T max values indicated that the mudstones were thermally immature-low maturity with mainly type II and III organic matter, while organic matter in marlite belongs mainly to type I-II1 with low maturity-maturity stage. The biomarkers showed the characteristics of odd-over-even predominance of long-chain n-alkanes, higher proportion of C27 sterane in most of the samples, heavy δ13Corg composition, low Pr/Ph ratios (0.11-0.36), and so on. Organic geochemistry indicated that the organic matter originated from bacteria, algae, and higher plants. The rocks were formed in reducing environments with stratified water column and high productivity. The paleoclimate became more humid during depositional stage in the western Hoh Xil basin.

Generic non-singular Poisson suspension is of type III1

AbstractIt is shown that for a dense $G_\delta $ -subset of the subgroup of non-singular transformations (of a standard infinite $\sigma $ -finite measure space) whose Poisson suspensions are non-singular, the corresponding Poisson suspensions are ergodic and of Krieger’s type III1.

External fluids cause alteration and metal redistribution in the granite-hosted Tangziwa Sn[sbnd]Cu deposit, Gejiu district, China

The granite-hosted Tangziwa SnCu deposit in the Gejiu district shows variable alteration of the granite with associated mineralization. In this paper, we used whole rock chemistry mass balance calculations and Sr, Nd, Pb, Li, and B isotope data to constrain the source of metals and fluids in different alteration stages. The δ7Li and δ11B values of unaltered and weakly altered (Type I) granite samples fall in narrow ranges of −0.70 to 3.61‰ and −14.87 to −12.82 ‰, respectively, which is typical for granites. The Li and B isotopic composition of moderately (Type II) to strongly altered (Type III-1 and Type III-2) granite samples are shifted toward higher δ7Li (up to 13.61‰) and lower δ11B values (as low as −31.32‰). These extreme values reflect the addition of Li and B via an external fluid. Petrographic observations and isocon mass balance calculations demonstrate that early stage, magmatic fluids altered biotite and plagioclase to muscovite and clay minerals, respectively, and led to loss of Ca, Na, Fe, and Cs. The later stage, external fluids caused the destruction of feldspar and the precipitation of calcite, anhydrite/gypsum, fluorite, and sulfide minerals (pyrite, chalcopyrite, arsenopyrite, and stannite). This alteration is associated with an increase in the contents of Ca, S, Fe, Co, Cu, Sb, Cd, and Sn and a reduction of the contents of Pb, Sr, Cs, and LREEs. The high contents of Cu and S, which are not typically abundant in granite, could be added by the external fluids characterized by high δ7Li and low δ11B. The weakly and moderately altered granites have lower Sn contents than the unaltered granite. This indicates that late magmatic or external fluids may have leached Sn from weakly and moderately altered granite and that sulfide minerals in the strongly altered granites eventually scavenged this mobilized Sn.