High-entropy materials(HEMs)have attracted considerable research attention in battery applications due to exceptional properties such as remarkable structural stability,enhanced ionic conductivity,superior mechanical ...High-entropy materials(HEMs)have attracted considerable research attention in battery applications due to exceptional properties such as remarkable structural stability,enhanced ionic conductivity,superior mechanical strength,and outstanding catalytic activity.These distinctive characteristics render HEMs highly suitable for various battery components,such as electrodes,electrolytes,and catalysts.This review systematically examines recent advances in the application of HEMs for energy storage,beginning with fundamental concepts,historical development,and key definitions.Three principal categories of HEMs,namely high-entropy alloys,high-entropy oxides,and highentropy MXenes,are analyzed with a focus on electrochemical performance metrics such as specific capacity,energy density,cycling stability,and rate capability.The underlying mechanisms by which these materials enhance battery performance are elucidated in the discussion.Furthermore,the pivotal role of machine learning in accelerating the discovery and optimization of novel high-entropy battery materials is highlighted.The review concludes by outlining future research directions and potential breakthroughs in HEM-based battery technologies.展开更多
High-entropy oxides(HEOs)have emerged as a promising class of memristive materials,characterized by entropy-stabilized crystal structures,multivalent cation coordination,and tunable defect landscapes.These intrinsic f...High-entropy oxides(HEOs)have emerged as a promising class of memristive materials,characterized by entropy-stabilized crystal structures,multivalent cation coordination,and tunable defect landscapes.These intrinsic features enable forming-free resistive switching,multilevel conductance modulation,and synaptic plasticity,making HEOs attractive for neuromorphic computing.This review outlines recent progress in HEO-based memristors across materials engineering,switching mechanisms,and synaptic emulation.Particular attention is given to vacancy migration,phase transitions,and valence-state dynamics—mechanisms that underlie the switching behaviors observed in both amorphous and crystalline systems.Their relevance to neuromorphic functions such as short-term plasticity and spike-timing-dependent learning is also examined.While encouraging results have been achieved at the device level,challenges remain in conductance precision,variability control,and scalable integration.Addressing these demands a concerted effort across materials design,interface optimization,and task-aware modeling.With such integration,HEO memristors offer a compelling pathway toward energy-efficient and adaptable brain-inspired electronics.展开更多
(NbZrHfTi)C high-entropy ceramics,as an emerging class of ultra-high-temperature materials,have garnered significant interest due to their unique multi-principal-element crystal structure and exceptional hightemperatu...(NbZrHfTi)C high-entropy ceramics,as an emerging class of ultra-high-temperature materials,have garnered significant interest due to their unique multi-principal-element crystal structure and exceptional hightemperature properties.This study systematically investigates the mechanical properties of(NbZrHfTi)C high-entropy ceramics by employing first-principles density functional theory,combined with the Debye-Grüneisen model,to explore the variations in their thermophysical properties with temperature(0–2000 K)and pressure(0–30 GPa).Thermodynamically,the calculated mixing enthalpy and Gibbs free energy confirm the feasibility of forming a stable single-phase solid solution in(NbZrHfTi)C.The calculated results of the elastic stiffness constant indicate that the material meets the mechanical stability criteria of the cubic crystal system,further confirming the structural stability.Through evaluation of key mechanical parameters—bulk modulus,shear modulus,Young’s modulus,and Poisson’s ratio—we provide comprehensive insight into the macro-mechanical behaviour of the material and its correlation with the underlying microstructure.Notably,compared to traditional binary carbides and their average properties,(NbZrHfTi)C exhibits higher Vickers hardness(Approximately 28.5 GPa)and fracture toughness(Approximately 3.4 MPa⋅m^(1/2)),which can be primarily attributed to the lattice distortion and solid-solution strengthening mechanism.The study also utilizes the quasi-harmonic approximation method to predict the material’s thermophysical properties,including Debye temperature(initial value around 563 K),thermal expansion coefficient(approximately 8.9×10^(−6) K−1 at 2000 K),and other key parameters such as heat capacity at constant volume.The results show that within the studied pressure and temperature ranges,(NbZrHfTi)C consistently maintains a stable phase structure and good thermomechanical properties.The thermal expansion coefficient increasing with temperature,while heat capacity approaches the Dulong-Petit limit at elevated temperatures.These findings underscore the potential of(NbZrHfTi)C applications in ultra-high temperature thermal protection systems,cutting tool coatings,and nuclear structural materials.展开更多
High entropy alloys(HEAs)have recently attracted significant attention due to their exceptional mechanical properties and potential applications across various fields.Friction stir welding and processing(FSW/P),as not...High entropy alloys(HEAs)have recently attracted significant attention due to their exceptional mechanical properties and potential applications across various fields.Friction stir welding and processing(FSW/P),as notable solid-state welding and processing techniques,have been proved effectiveness in enhancing microstructures and mechanical properties of HEAs.This review article summarizes the current status of FSW/P of HEAs.The welding materials and conditions used for FSW/P in HEAs are reviewed and discussed.The effects of FSW/P on the evolutions of grain structure,texture,dislocation,and secondary phase for different HEAs are highlighted.Furthermore,the influences of FSW/P on the mechanical properties of various HEAs are analyzed.Finally,potential applications,challenges,and future directions of FSW/P in HEAs are forecasted.Overall,FSW/P enable to refine grains of HEAs through dynamic recrystallization and to activate diverse deformation mechanisms of HEAs through tailoring phase structures,thereby significantly improving the strength,hardness,and ductility of both single-and dual-phase HEAs.Future progress in this field will rely on comprehensive optimization of processing parameters and alloy composition,integration of multi-scale modeling with advanced characterization for in-depth exploration of microstructural mechanisms,systematic evaluation of functional properties,and effective bridging of the gap between laboratory research and industrial application.The review aims to provide an overview of recent advancements in the FSW/P of HEAs and encourage further research in this area.展开更多
High‐entropy amorphous catalysts(HEACs)integrate multielement synergy with structural disorder,making them promising candidates for water splitting.Their distinctive features—including flexible coordination environm...High‐entropy amorphous catalysts(HEACs)integrate multielement synergy with structural disorder,making them promising candidates for water splitting.Their distinctive features—including flexible coordination environments,tunable electronic structures,abundant unsaturated active sites,and dynamic structural reassembly—collectively enhance electrochemical activity and durability under operating conditions.This review summarizes recent advances in HEACs for hydrogen evolution,oxygen evolution,and overall water splitting,highlighting their disorder-driven advantages over crystalline counterparts.Catalytic performance benchmarks are presented,and mechanistic insights are discussed,focusing on how multimetallic synergy,amorphization effect,and in‐situ reconstruction cooperatively regulate reaction pathways.These insights provide guidance for the rational design of next‐generation amorphous high‐entropy electrocatalysts with improved efficiency and durability.展开更多
The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entro...The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Fhrther it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole＇s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.展开更多
The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limi...The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.展开更多
Elements of correspondence (“coincidences”) between a student’s solutions to an assigned set of quantitative problems and the solutions manual for the course textbook may suggest that the stu-dent copied the work f...Elements of correspondence (“coincidences”) between a student’s solutions to an assigned set of quantitative problems and the solutions manual for the course textbook may suggest that the stu-dent copied the work from an illicit source. Plagiarism of this kind, which occurs primarily in fields such as the natural sciences, engineering, and mathematics, is often difficult to establish. This paper derives an expression for the probability that alleged coincidences in a student’s paper could be attributable to pure chance. The analysis employs the Principle of Maximum Entropy (PME), which, mathematically, is a variational procedure requiring maximization of the Shannon-Jaynes entropy function augmented by the completeness relation for probabilities and known information in the form of expectation values. The virtue of the PME as a general method of inferential reasoning is that it generates the most objective (i.e. least biased) probability distribution consistent with the given information. Numerical examination of test cases for a range of plausible conditions can yield outcomes that tend to exonerate a student who otherwise might be wrongfully judged guilty of cheating by adjudicators unfamiliar with the surprising properties of random processes.展开更多
This paper concerns an application of a popular existing law, the maximum entropy principle, to the study of statistical distribution of the ocean wave heights. Under two proper premisses. a conclusion that the wave h...This paper concerns an application of a popular existing law, the maximum entropy principle, to the study of statistical distribution of the ocean wave heights. Under two proper premisses. a conclusion that the wave heights obey the Weibull distribution is drawn by making use of the maximum entropy principle. From this result, we hold that the intnnsic departures using the Rayleigh distribution to describe The realistic wave height must exist, and the Weibull distribution usually used as an empirical one has profound origin in physics. The Gluhovskli's empirical wave heights distribution relying on water depth is also discussed briefly, and a possible physical explanation associated with the maximum entropy principle is carried out.展开更多
The iron and steel industry in China has experienced vast changes over the past thirty years.To have a precise knowledge of the circumstances behind its evolution,it is essential to perform an iron flow analysis.Accor...The iron and steel industry in China has experienced vast changes over the past thirty years.To have a precise knowledge of the circumstances behind its evolution,it is essential to perform an iron flow analysis.Accordingly,iron flow analysis for the years 1990-2015 was conducted.Firstly,the iron natural resource efficiency,Chinese steel scrap index,and Chinese iron ore support ratio which can reflect the running status of China's iron and steel industry for these six years(1990,1995,2000,2005,2010,and 2015)were analyzed;thereafter,value chain and statistical entropy analyses were conducted based on the iron flow analysis,and some interesting results were obtained.Discussions and conclusions based on the results along with the recommendations for the China's iron and industry were proposed.展开更多
The total quantum statistical entropy of Reissner-Nordstrom black holes inDirac field case is evaluated in this article. The space-time of the black holes is divided intothree regions: region 1 (r 】 r_o), region 2 (r...The total quantum statistical entropy of Reissner-Nordstrom black holes inDirac field case is evaluated in this article. The space-time of the black holes is divided intothree regions: region 1 (r 】 r_o), region 2 (r_o 】 r 】 r_i), and region 3 (r_i 】 r 】 0), where r_ois the radius of the outer event horizon, and Ti is the radius of the inner event horizon. The totalquantum statistical entropy of Reissner-Nordstrom black holes is S = S_1 + S_2 + S_3, where S_i (i= 1,2,3) is the entropy, contributed by regions 1,2,3. The detailed calculation shows that S_2 isneglectfully small. S_1 = w_t(π~2/45)k_b(A_o/ε~2β~3), S_3 = -w_t(π~2/45)k_b(A_i/ε~2β~3), whereA_o and A_i are, respectively, the areas of the outer and inner event horizons, w_t = 2~s[1 -2~(-(s+1))], s = d/2, d is the space-time dimension, here d = 4, s = 2. As r_i approaches r_o in theextreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approacheszero.展开更多
Biology without governing principle makes predications impossible. Observations lead to some successful therapies, and to unexpected failures. Erwin Schr<span style="white-space:nowrap;">ö<...Biology without governing principle makes predications impossible. Observations lead to some successful therapies, and to unexpected failures. Erwin Schr<span style="white-space:nowrap;">ö</span>dinger attempted to quantify biology with the concept of negative entropy. These insights lead to fundamental principles of biologic entropy. The quantification of negative entropy is difficult to calculate since the number of parts of the body and the way these parts are arranged is very large (atomistic disorder). There can be approximations that answer questions such as why females live longer, and why a lower body temperature predicts longevity. This concept can reveal the culprit of diabetes II;understanding the microbiome can reduce its entropy by increasing the entropy of its host. The real advantage of statistical entropy is finding new drugs and predicting viral mutations based on energetics and negative entropy. The misfolding of a protein will increase the entropy of an individual with the result of early death. The calculations of biologic entropy require the knowledge of each developmental step, and the statistical possibilities of the next step. If the step is crucial to maintain low entropy, a carrier protein will assure the energetics of the step is favorable. This protein is the target of new therapies.展开更多
The aim of this study is to understand and quantify the urban growth and trend in Zarqa city during the period 1990 to 2014 and to produce land use and cover map for the studied area through the use of the GIS and rem...The aim of this study is to understand and quantify the urban growth and trend in Zarqa city during the period 1990 to 2014 and to produce land use and cover map for the studied area through the use of the GIS and remote sensing techniques with Shannon’s Entropy statistical method. For this purpose, three Landsat images were used for land use classification by using supervised maximum likelihood classification techniques to extract and assess the changes of urban lands. The results indicated that the urban areas in Zarqa city increased by 22.15% in the period from 1990 to 2005 and 14.86% from 2005 to 2014, with a rate of expansion of 0.96 and by 1.31 km<sup>2</sup>/ year for the two time periods respectively. The entropy value increased from 1.20 in the first period to 1.38 in the second, while the entropy value for the NE, NW, SE and SW zones showed high values, which confirmed that urban expansion and sprawling had existed in the past twenty four years in the study area. Urban expansion and sprawl cause different impacts on the natural, economic, and aesthetic aspects of the city which lead and guide government officials and planners to understand and monitor current growth and visualize future growth.展开更多
Ey means of conformal Held theory,we have related the degrees of freedom of microstates to the entropy of three-dimensional charged black hole as well as the entanglement entropy of three-dimensional De Sitter spaceti...Ey means of conformal Held theory,we have related the degrees of freedom of microstates to the entropy of three-dimensional charged black hole as well as the entanglement entropy of three-dimensional De Sitter spacetime,We have shown that the degrees of freedom of the conformal theory responsible for the entropy represent states on the horizon and localized in physical spacetime.展开更多
In recent years,medium entropy alloys have become a research hotspot due to their excellent physical and chemical performances.By controlling reasonable elemental composition and processing parameters,the medium entro...In recent years,medium entropy alloys have become a research hotspot due to their excellent physical and chemical performances.By controlling reasonable elemental composition and processing parameters,the medium entropy alloys can exhibit similar properties to high entropy alloys and have lower costs.In this paper,a FeCoNi medium entropy alloy precursor was prepared via sol-gel and coprecipitation methods,respectively,and FeCoNi medium entropy alloys were prepared by carbothermal and hydrogen reduction.The phases and magnetic properties of FeCoNi medium entropy alloy were investigated.Results showed that FeCoNi medium entropy alloy was produced by carbothermal and hydrogen reduction at 1500℃.Some carbon was detected in the FeCoNi medium entropy alloy prepared by carbothermal reduction.The alloy prepared by hydrogen reduction was uniform and showed a relatively high purity.Moreover,the hydrogen reduction product exhibited better saturation magnetization and lower coercivity.展开更多
The statistical entropy of the Kaluza-Klein black hole is studied by counting the black hole states which form an algebra of diffeomorphism at Killing horizon with a central charge.It is shown that the entropy yielded...The statistical entropy of the Kaluza-Klein black hole is studied by counting the black hole states which form an algebra of diffeomorphism at Killing horizon with a central charge.It is shown that the entropy yielded by the standard Cardy formula agrees with the Bekenstein-Hawking entropy only if we take period T of function u as the periodicity of the Euclidean black hole.On the other hand,the first-order quantum correction to the entropy is proportional to logarithm of the Bekenstein-Hawking entropy with a factor-1/2.展开更多
The free energy and entropy of a general spherically symmetry black hole are calculated by quantum statistic method with brick wall model Two different kinds of approximation are used to calculate the number of states...The free energy and entropy of a general spherically symmetry black hole are calculated by quantum statistic method with brick wall model Two different kinds of approximation are used to calculate the number of states in transverse spatial space. The final results are approximately equal except a rational numerical constant. The formulas of free energy and entropy, evaluated by each one of the two different kinds of approximation, are the same except some numerical constants. The free energy and entropy are dependent on the spacetime dimensionsD. When D = 4, they reduce to the usual well known results.展开更多
The total quantum statistical entropy of Reissner-Nordstrom (RN) black holes is evaluated. The spacetime of the black holes is divided into three regions-region 1, (r > ro);region 2, (ro > r > ri);andregion 3...The total quantum statistical entropy of Reissner-Nordstrom (RN) black holes is evaluated. The spacetime of the black holes is divided into three regions-region 1, (r > ro);region 2, (ro > r > ri);andregion 3, (ri > r > 0)-where ro is the radius of the outer event horizon, and ri is the radius of the inner event horizon. The total quantum statistical entropy of RN black holes is S = S1 + S2 + Ss, where Si (i = 1, 2, 3) is the entropy, contributed by region Si (i = 1, 2, 3). The detailed calculation shows that S2 ≈ 0. S1 = (π^(2)/45)[kbAo/∈^(2)β^(3)], S3 = -(r2/45)[kbAi/∈^(2)β^(3)], where Ao and Ai are, respectively, the area of the outer and inner event horizons. Thus, as ri approaches ro, in the extreme case the total quantum statistical entropy of RN black holes approaches zero.展开更多
Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensio...Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensions, we calculate the statistical entropy of the scalar field in the higher-dimensional static spherically symmetric black hole spacetime without any artificial cutoff. Calculation shows that the entropy is proportional to the horizon area. The coefficient of proportionality is 1/4 when the minimal length parameter is selected appropriately.展开更多
基金supported by the Fujian Provincial Science and Technology Planning Project(No.2022HZ027006,No.2024HZ021023)National Natural Science Foundation of China(No.U22A20118).
文摘High-entropy materials(HEMs)have attracted considerable research attention in battery applications due to exceptional properties such as remarkable structural stability,enhanced ionic conductivity,superior mechanical strength,and outstanding catalytic activity.These distinctive characteristics render HEMs highly suitable for various battery components,such as electrodes,electrolytes,and catalysts.This review systematically examines recent advances in the application of HEMs for energy storage,beginning with fundamental concepts,historical development,and key definitions.Three principal categories of HEMs,namely high-entropy alloys,high-entropy oxides,and highentropy MXenes,are analyzed with a focus on electrochemical performance metrics such as specific capacity,energy density,cycling stability,and rate capability.The underlying mechanisms by which these materials enhance battery performance are elucidated in the discussion.Furthermore,the pivotal role of machine learning in accelerating the discovery and optimization of novel high-entropy battery materials is highlighted.The review concludes by outlining future research directions and potential breakthroughs in HEM-based battery technologies.
基金financially supported by the National Natural Science Foundation of China(Grant No.12172093)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2021A1515012607)。
文摘High-entropy oxides(HEOs)have emerged as a promising class of memristive materials,characterized by entropy-stabilized crystal structures,multivalent cation coordination,and tunable defect landscapes.These intrinsic features enable forming-free resistive switching,multilevel conductance modulation,and synaptic plasticity,making HEOs attractive for neuromorphic computing.This review outlines recent progress in HEO-based memristors across materials engineering,switching mechanisms,and synaptic emulation.Particular attention is given to vacancy migration,phase transitions,and valence-state dynamics—mechanisms that underlie the switching behaviors observed in both amorphous and crystalline systems.Their relevance to neuromorphic functions such as short-term plasticity and spike-timing-dependent learning is also examined.While encouraging results have been achieved at the device level,challenges remain in conductance precision,variability control,and scalable integration.Addressing these demands a concerted effort across materials design,interface optimization,and task-aware modeling.With such integration,HEO memristors offer a compelling pathway toward energy-efficient and adaptable brain-inspired electronics.
基金supported by the National Natural Science Foundation of China(Nos.92166105 and 52005053)High-Tech Industry Science and Technology Innovation Leading Program of Hunan Province(No.2020GK2085)the Science and Technology Innovation Program of Hunan Province(No.2021RC3096).
文摘(NbZrHfTi)C high-entropy ceramics,as an emerging class of ultra-high-temperature materials,have garnered significant interest due to their unique multi-principal-element crystal structure and exceptional hightemperature properties.This study systematically investigates the mechanical properties of(NbZrHfTi)C high-entropy ceramics by employing first-principles density functional theory,combined with the Debye-Grüneisen model,to explore the variations in their thermophysical properties with temperature(0–2000 K)and pressure(0–30 GPa).Thermodynamically,the calculated mixing enthalpy and Gibbs free energy confirm the feasibility of forming a stable single-phase solid solution in(NbZrHfTi)C.The calculated results of the elastic stiffness constant indicate that the material meets the mechanical stability criteria of the cubic crystal system,further confirming the structural stability.Through evaluation of key mechanical parameters—bulk modulus,shear modulus,Young’s modulus,and Poisson’s ratio—we provide comprehensive insight into the macro-mechanical behaviour of the material and its correlation with the underlying microstructure.Notably,compared to traditional binary carbides and their average properties,(NbZrHfTi)C exhibits higher Vickers hardness(Approximately 28.5 GPa)and fracture toughness(Approximately 3.4 MPa⋅m^(1/2)),which can be primarily attributed to the lattice distortion and solid-solution strengthening mechanism.The study also utilizes the quasi-harmonic approximation method to predict the material’s thermophysical properties,including Debye temperature(initial value around 563 K),thermal expansion coefficient(approximately 8.9×10^(−6) K−1 at 2000 K),and other key parameters such as heat capacity at constant volume.The results show that within the studied pressure and temperature ranges,(NbZrHfTi)C consistently maintains a stable phase structure and good thermomechanical properties.The thermal expansion coefficient increasing with temperature,while heat capacity approaches the Dulong-Petit limit at elevated temperatures.These findings underscore the potential of(NbZrHfTi)C applications in ultra-high temperature thermal protection systems,cutting tool coatings,and nuclear structural materials.
基金supported by National Natural Science Foundation of China(Grant No.52171032)Hebei Natural Science Foundation(Grant No.E2023501002)Fundamental Research Funds for the Central Universities(Grant No.2024GFYD003)。
文摘High entropy alloys(HEAs)have recently attracted significant attention due to their exceptional mechanical properties and potential applications across various fields.Friction stir welding and processing(FSW/P),as notable solid-state welding and processing techniques,have been proved effectiveness in enhancing microstructures and mechanical properties of HEAs.This review article summarizes the current status of FSW/P of HEAs.The welding materials and conditions used for FSW/P in HEAs are reviewed and discussed.The effects of FSW/P on the evolutions of grain structure,texture,dislocation,and secondary phase for different HEAs are highlighted.Furthermore,the influences of FSW/P on the mechanical properties of various HEAs are analyzed.Finally,potential applications,challenges,and future directions of FSW/P in HEAs are forecasted.Overall,FSW/P enable to refine grains of HEAs through dynamic recrystallization and to activate diverse deformation mechanisms of HEAs through tailoring phase structures,thereby significantly improving the strength,hardness,and ductility of both single-and dual-phase HEAs.Future progress in this field will rely on comprehensive optimization of processing parameters and alloy composition,integration of multi-scale modeling with advanced characterization for in-depth exploration of microstructural mechanisms,systematic evaluation of functional properties,and effective bridging of the gap between laboratory research and industrial application.The review aims to provide an overview of recent advancements in the FSW/P of HEAs and encourage further research in this area.
基金supported by the Australian Research Council(ARC)Projects(DP220101139,DP220101142,and LP240100542).
文摘High‐entropy amorphous catalysts(HEACs)integrate multielement synergy with structural disorder,making them promising candidates for water splitting.Their distinctive features—including flexible coordination environments,tunable electronic structures,abundant unsaturated active sites,and dynamic structural reassembly—collectively enhance electrochemical activity and durability under operating conditions.This review summarizes recent advances in HEACs for hydrogen evolution,oxygen evolution,and overall water splitting,highlighting their disorder-driven advantages over crystalline counterparts.Catalytic performance benchmarks are presented,and mechanistic insights are discussed,focusing on how multimetallic synergy,amorphization effect,and in‐situ reconstruction cooperatively regulate reaction pathways.These insights provide guidance for the rational design of next‐generation amorphous high‐entropy electrocatalysts with improved efficiency and durability.
基金The project supported by National Natural Science Foundation of China under Grant No. 10374075 and Natural Science Foundation of Shanxi Province of China under Grant No. 20001009
文摘The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Fhrther it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole＇s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.
基金This work was financially supported by the National Natural Science Foundation of China (Grant No50479028)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No20060423009)
文摘The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.
文摘Elements of correspondence (“coincidences”) between a student’s solutions to an assigned set of quantitative problems and the solutions manual for the course textbook may suggest that the stu-dent copied the work from an illicit source. Plagiarism of this kind, which occurs primarily in fields such as the natural sciences, engineering, and mathematics, is often difficult to establish. This paper derives an expression for the probability that alleged coincidences in a student’s paper could be attributable to pure chance. The analysis employs the Principle of Maximum Entropy (PME), which, mathematically, is a variational procedure requiring maximization of the Shannon-Jaynes entropy function augmented by the completeness relation for probabilities and known information in the form of expectation values. The virtue of the PME as a general method of inferential reasoning is that it generates the most objective (i.e. least biased) probability distribution consistent with the given information. Numerical examination of test cases for a range of plausible conditions can yield outcomes that tend to exonerate a student who otherwise might be wrongfully judged guilty of cheating by adjudicators unfamiliar with the surprising properties of random processes.
文摘This paper concerns an application of a popular existing law, the maximum entropy principle, to the study of statistical distribution of the ocean wave heights. Under two proper premisses. a conclusion that the wave heights obey the Weibull distribution is drawn by making use of the maximum entropy principle. From this result, we hold that the intnnsic departures using the Rayleigh distribution to describe The realistic wave height must exist, and the Weibull distribution usually used as an empirical one has profound origin in physics. The Gluhovskli's empirical wave heights distribution relying on water depth is also discussed briefly, and a possible physical explanation associated with the maximum entropy principle is carried out.
基金supported by the National Key Research and Development Program of China(2019YFC1905204)the Soft Science Program Funded by Fujian Provincial Department of Science and Technology(2019R0067)+1 种基金the Project of Sichuan Mineral Resources Research Center(SCKCZY2020-YB01)the Fundamental Research Funds for the Central Universities of China(N182502045).
文摘The iron and steel industry in China has experienced vast changes over the past thirty years.To have a precise knowledge of the circumstances behind its evolution,it is essential to perform an iron flow analysis.Accordingly,iron flow analysis for the years 1990-2015 was conducted.Firstly,the iron natural resource efficiency,Chinese steel scrap index,and Chinese iron ore support ratio which can reflect the running status of China's iron and steel industry for these six years(1990,1995,2000,2005,2010,and 2015)were analyzed;thereafter,value chain and statistical entropy analyses were conducted based on the iron flow analysis,and some interesting results were obtained.Discussions and conclusions based on the results along with the recommendations for the China's iron and industry were proposed.
文摘The total quantum statistical entropy of Reissner-Nordstrom black holes inDirac field case is evaluated in this article. The space-time of the black holes is divided intothree regions: region 1 (r 】 r_o), region 2 (r_o 】 r 】 r_i), and region 3 (r_i 】 r 】 0), where r_ois the radius of the outer event horizon, and Ti is the radius of the inner event horizon. The totalquantum statistical entropy of Reissner-Nordstrom black holes is S = S_1 + S_2 + S_3, where S_i (i= 1,2,3) is the entropy, contributed by regions 1,2,3. The detailed calculation shows that S_2 isneglectfully small. S_1 = w_t(π~2/45)k_b(A_o/ε~2β~3), S_3 = -w_t(π~2/45)k_b(A_i/ε~2β~3), whereA_o and A_i are, respectively, the areas of the outer and inner event horizons, w_t = 2~s[1 -2~(-(s+1))], s = d/2, d is the space-time dimension, here d = 4, s = 2. As r_i approaches r_o in theextreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approacheszero.
文摘Biology without governing principle makes predications impossible. Observations lead to some successful therapies, and to unexpected failures. Erwin Schr<span style="white-space:nowrap;">ö</span>dinger attempted to quantify biology with the concept of negative entropy. These insights lead to fundamental principles of biologic entropy. The quantification of negative entropy is difficult to calculate since the number of parts of the body and the way these parts are arranged is very large (atomistic disorder). There can be approximations that answer questions such as why females live longer, and why a lower body temperature predicts longevity. This concept can reveal the culprit of diabetes II;understanding the microbiome can reduce its entropy by increasing the entropy of its host. The real advantage of statistical entropy is finding new drugs and predicting viral mutations based on energetics and negative entropy. The misfolding of a protein will increase the entropy of an individual with the result of early death. The calculations of biologic entropy require the knowledge of each developmental step, and the statistical possibilities of the next step. If the step is crucial to maintain low entropy, a carrier protein will assure the energetics of the step is favorable. This protein is the target of new therapies.
文摘The aim of this study is to understand and quantify the urban growth and trend in Zarqa city during the period 1990 to 2014 and to produce land use and cover map for the studied area through the use of the GIS and remote sensing techniques with Shannon’s Entropy statistical method. For this purpose, three Landsat images were used for land use classification by using supervised maximum likelihood classification techniques to extract and assess the changes of urban lands. The results indicated that the urban areas in Zarqa city increased by 22.15% in the period from 1990 to 2005 and 14.86% from 2005 to 2014, with a rate of expansion of 0.96 and by 1.31 km<sup>2</sup>/ year for the two time periods respectively. The entropy value increased from 1.20 in the first period to 1.38 in the second, while the entropy value for the NE, NW, SE and SW zones showed high values, which confirmed that urban expansion and sprawling had existed in the past twenty four years in the study area. Urban expansion and sprawl cause different impacts on the natural, economic, and aesthetic aspects of the city which lead and guide government officials and planners to understand and monitor current growth and visualize future growth.
基金supported by the National Natural Science Foundation of China under Grant No.19975010supported by the National Natural Science Foundation of China under Grant No.19805004.
文摘Ey means of conformal Held theory,we have related the degrees of freedom of microstates to the entropy of three-dimensional charged black hole as well as the entanglement entropy of three-dimensional De Sitter spacetime,We have shown that the degrees of freedom of the conformal theory responsible for the entropy represent states on the horizon and localized in physical spacetime.
基金financially supported by the National Natural Science Foundation of China(Nos.52074078 and 52374327)the Applied Fundamental Research Program of Liaoning Province,China(No.2023JH2/101600002)+3 种基金the Liaoning Provincial Natural Science Foundation,China(No.2022-YQ-09)the Shenyang Young Middle-Aged Scientific and Technological Innovation Talent Support Program,China(No.RC220491)the Liaoning Province Steel Industry-University-Research Innovation Alliance Cooperation Project of Bensteel Group,China(No.KJBLM202202)the Fundamental Research Funds for the Central Universities,China(Nos.N2201023 and N2325009)。
文摘In recent years,medium entropy alloys have become a research hotspot due to their excellent physical and chemical performances.By controlling reasonable elemental composition and processing parameters,the medium entropy alloys can exhibit similar properties to high entropy alloys and have lower costs.In this paper,a FeCoNi medium entropy alloy precursor was prepared via sol-gel and coprecipitation methods,respectively,and FeCoNi medium entropy alloys were prepared by carbothermal and hydrogen reduction.The phases and magnetic properties of FeCoNi medium entropy alloy were investigated.Results showed that FeCoNi medium entropy alloy was produced by carbothermal and hydrogen reduction at 1500℃.Some carbon was detected in the FeCoNi medium entropy alloy prepared by carbothermal reduction.The alloy prepared by hydrogen reduction was uniform and showed a relatively high purity.Moreover,the hydrogen reduction product exhibited better saturation magnetization and lower coercivity.
基金Supported in part by the National Natural Science Foundation of China under grant No.19975018.
文摘The statistical entropy of the Kaluza-Klein black hole is studied by counting the black hole states which form an algebra of diffeomorphism at Killing horizon with a central charge.It is shown that the entropy yielded by the standard Cardy formula agrees with the Bekenstein-Hawking entropy only if we take period T of function u as the periodicity of the Euclidean black hole.On the other hand,the first-order quantum correction to the entropy is proportional to logarithm of the Bekenstein-Hawking entropy with a factor-1/2.
文摘The free energy and entropy of a general spherically symmetry black hole are calculated by quantum statistic method with brick wall model Two different kinds of approximation are used to calculate the number of states in transverse spatial space. The final results are approximately equal except a rational numerical constant. The formulas of free energy and entropy, evaluated by each one of the two different kinds of approximation, are the same except some numerical constants. The free energy and entropy are dependent on the spacetime dimensionsD. When D = 4, they reduce to the usual well known results.
文摘The total quantum statistical entropy of Reissner-Nordstrom (RN) black holes is evaluated. The spacetime of the black holes is divided into three regions-region 1, (r > ro);region 2, (ro > r > ri);andregion 3, (ri > r > 0)-where ro is the radius of the outer event horizon, and ri is the radius of the inner event horizon. The total quantum statistical entropy of RN black holes is S = S1 + S2 + Ss, where Si (i = 1, 2, 3) is the entropy, contributed by region Si (i = 1, 2, 3). The detailed calculation shows that S2 ≈ 0. S1 = (π^(2)/45)[kbAo/∈^(2)β^(3)], S3 = -(r2/45)[kbAi/∈^(2)β^(3)], where Ao and Ai are, respectively, the area of the outer and inner event horizons. Thus, as ri approaches ro, in the extreme case the total quantum statistical entropy of RN black holes approaches zero.
基金Supported by the Graduate Student Creative Foundation of Hunan University of Science and Technology under Grant No S080111, Scientific Research Foundation for the Returned Overseas Chinese Scholars from State Education Ministry of China under Grant No 527[2004]） and the Hunan Provincial Natural Science Foundation under Grant No 06JJ2026.
文摘Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensions, we calculate the statistical entropy of the scalar field in the higher-dimensional static spherically symmetric black hole spacetime without any artificial cutoff. Calculation shows that the entropy is proportional to the horizon area. The coefficient of proportionality is 1/4 when the minimal length parameter is selected appropriately.
