Entropy Method Research Articles

Entropy Considerations in Stochastic Electrodynamics

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations that have been fully carried out to date are discussed in two main cases: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, or Rayleigh–Jeans radiation; and second, where only these radiation fields exist within a cavity. The emphasis here is on the first, more complicated, case, where both charged particles and radiation fields are present and interacting. Unlike the usual exposition on entropy in classical statistical mechanics, involving probabilistic notions of phase-space occupation, the calculations to date for both particles and fields, or for fields alone, follow the caloric entropy method, where the notions of heat flow, adiabatic surfaces, and isothermal conditions are utilized. Probability notions certainly still enter into the calculations, as the fields and charged particles interact stochastically together, following Maxwellian electrodynamics. Examples of phase-space calculations for harmonic oscillators and classical hydrogen atoms are carried out, emphasizing how much farther caloric entropy calculations have successfully gone.

Anchoring temporal convolutional networks for epileptic seizure prediction.

Accurate and timely prediction of epileptic seizures is crucial for empowering patients to mitigate their impact or prevent them altogether. Current studies predominantly focus on short-term seizure predictions, which causes the prediction time to be shorter than the onset of antiepileptic, thus failing to prevent seizures. However, longer epilepsy prediction faces the problem that as the preictal period lengthens, it increasingly resembles the interictal period, complicating differentiation. To address these issues, we employ the sample entropy method for feature extraction from electroencephalography (EEG) signals. Subsequently, we introduce the Anchoring Temporal Convolutional Networks (ATCN) model for longer-term, patient-specific epilepsy prediction. ATCN utilizes dilated causal convolutional networks to learn time-dependent features from previous data, capturing temporal causal correlations within and between samples. Additionally, the model also incorporates anchoring data to enhance the performance of epilepsy prediction further. Finally, we proposed a multilayer sliding window prediction algorithm for seizure alarms. Evaluation on the Freiburg intracranial EEG dataset shows our approach achieves 100% sensitivity, a false prediction rate (FPR) of 0.08 per hour and an average prediction time (APT) of 99.98 minutes. Using the CHB-MIT scalp EEG dataset, we a achieve 97.44% sensitivity, an FPR of 0.11 per hour, and an APT of 92.99 minutes. These results demonstrate that our approach is adequate for seizure prediction over a more extended prediction range on intracranial and scalp EEG datasets. The average prediction time of our approach exceeds the typical onset time of antiepileptic. This approach is particularly beneficial for patients who need to take medication at regular intervals, as they may only need to take their medication when our method issues an alarm. This capability has the potential to prevent seizures, which will greatly improving patients' quality of life.

Quantitative evidence of the community of shared future for mankind as a driver of sustainable development in human society

In an era marked by global economic challenges, an increasing array of non-traditional security threats, and a proliferation of conflicts and issues, China has put forth the building of a community of shared future for mankind as a way to address this question of the times. The theory of the community of shared future for mankind offers a framework to address contemporary issues by promoting equality, mutual benefit, security, justice, openness, innovation, multicultural exchange, and green development. This paper innovatively quantifies the five core principles of the theory of the community of shared future for mankind using the entropy method. It calculates the proxy variable for sustainable development, green total factor productivity, using the super-efficiency Slack-Based Measure model in Data Envelopment Analysis. Baseline regression is conducted on this basis. The Principal Component Analysis method and another Data Envelopment Analysis method, the Malmquist index, are utilized to recalculate the indicators, followed by another round of regression analysis. The results are consistent with the baseline regression. Additionally, Ordinary Least Squares, Partial Least Squares, Maximum Likelihood Estimation, Ridge regression, and Lasso regression are employed to ensure the robustness of the results. The findings indicate a significant positive relationship between the community of a shared future for mankind and the sustainable development of human society, with consistent conclusions drawn from different calculation methods and regression techniques. Through value recognition, international cooperation based on benefit-sharing and mutual reciprocity can guide humanity towards a harmonious coexistence with nature, irrespective of regional and economic disparities. This study provides quantitative evidence of the impact of the community of a shared future for mankind on the sustainable development of human society, filling a gap in existing research. Based on these findings, feasible policy recommendations are proposed to promote sustainable development in human society.

Analysis of Factors Affecting the Spatial Association Network of Food Security Level in China

Food security serves as the cornerstone of national security, intricately linked to social stability and economic progress. Currently, with the swift evolutions in social economy, logistics and transport, information dissemination, and technological advancements, there has been a marked increase in the cross-regional flow of food production, distribution, and consumption. Consequently, the spatial interdependence of food security across different regions has grown increasingly salient. This paper investigates the spatial interrelationship of food security levels in China through a network analysis framework, examining its determinants and network dynamics. The findings offer valuable insights for decision-makers aiming to optimize agricultural resource allocation and enhance national food security levels. This research establishes a comprehensive evaluation index system for assessing food security levels in China across four dimensions: production security, distribution security, supply security, and consumption security. Employing data from 30 provinces between 2008 and 2022, the entropy method quantifies food security levels, while a modified gravity model underpins the construction of a spatial association network. This framework subsequently examines the network’s structural characteristics and the factors influencing its formation. The results reveal that: (1) China’s food security levels demonstrate a consistent upward trajectory over the study period, though significant regional disparities persist. The central region surpasses the national average, while the eastern and western regions lag. Recently, the western region has shown accelerated improvements in food security, followed by the central area, with the eastern region maintaining steady growth. (2) A structurally robust spatial correlation network of food security has emerged, characterized by variations in the number of network relationships, fluctuations in network density, and a decline in network efficiency while still exhibiting pronounced small-world characteristics. (3) The network displays a clear core-periphery structure, with Shanghai, Beijing, and Jiangsu positioned centrally, playing pivotal intermediary roles, whereas remote provinces such as Gansu, Ningxia, and Liaoning occupy the periphery. (4) The four major regions demonstrate sparse internal connectivity yet robust inter-regional ties, resulting in pronounced spillover effects. (5) Various factors, including geographic distance, provincial proximity, disparities in economic development levels, variations in marketization, differences in agricultural human capital, and disparities in land productivity, significantly impact the establishment of spatial correlations in food security. The affirmative influences of geographic distance and neighboring relations, along with the beneficial shifts in economic development disparities, suggest that the flow of technology and resources plays a crucial role in reinforcing spatial connections.

The Coupling Coordination Relationship and Driving Factors of the Digital Economy and High-Quality Development of Rural Tourism: Insights from Chinese Experience Data

Globally, rural tourism development faces challenges such as inadequate infrastructure, insufficient marketing resources, and unreliable service quality, all of which limit its potential. However, digital technology offers unprecedented opportunities to address these barriers. China’s experience in integrating digital technology into rural tourism provides a valuable case study for understanding the digitalization of rural tourism. This study constructs an index system to assess the coupling coordination relationship between the digital economy and the high-quality development of rural tourism (HQDRT). By employing methods such as the entropy method, coupling coordination degree model, obstacle factor model, and geographic detector, the study examines the evolution of this coupling coordination relationship and its driving mechanisms across 31 provinces (including regions and municipalities) in China from 2012 to 2021. The findings reveal that (1) The development of the digital economy generally lags behind that of the rural tourism, but the coupling coordination relationship between the two is steadily improving. (2) The level of coupling coordination increases from west to east, with spatial distribution patterns evolving from ‘antagonism’ to ‘adaptation’ and then to ‘coordination’ as they move eastward. Most provinces belong to the ‘adaptation’ type. (3) From a nationwide perspective, the primary obstacles impeding the development of the digital economy include an insufficient internet penetration rate, which consequently leads to underdeveloped internet finance development and telecommunications industry development. The major barriers to the HQDRT stem from an inadequate number of tourists and a lack of physical infrastructure. (4) Population density, consumer spending, and R&D are significant drivers of the coupling coordination relationship, with the interaction between urbanization rates and other factors generally weakening the degree of coupling.

Research on underwater target signal orientation estimation based on smoothness priors approach

Purpose This paper aims to address the challenges in hydroacoustic signal detection, signal distortion and target localization caused by baseline drift. The authors propose a combined algorithm that integrates short-time Fourier transform (STFT) detection, smoothness priors approach (SPA), attitude calibration and direction of arrival (DOA) estimation for micro-electro-mechanical system vector hydrophones. Design/methodology/approach Initially, STFT method screens target signals with baseline drift in low signal-to-noise ratio environments, facilitating easier subsequent processing. Next, SPA is applied to the screened target signal, effectively removing the baseline drift, and combined with filtering to improve the signal-to-noise ratio. Then, vector channel amplitudes are corrected using attitude correction with 2D compass data. Finally, the absolute target azimuth is estimated using the minimum variance distortion-free response beamformer. Findings Simulation and experimental results demonstrate that the SPA outperforms high-pass filtering in removing baseline drift and is comparable to the effectiveness of variational mode decomposition, with significantly shorter processing times, making it more suitable for real-time applications. The detection performance of the STFT method is superior to instantaneous correlation detection and sample entropy methods. The final DOA estimation achieves an accuracy within 2°, enabling precise target azimuth estimation. Originality/value To the best of the authors’ knowledge, this study is the first to apply SPA to baseline drift removal in hydroacoustic signals, significantly enhancing the efficiency and accuracy of signal processing. It demonstrates the method’s outstanding performance in the field of underwater signal processing. In addition, it confirms the reliability and feasibility of STFT for signal detection in the presence of baseline drift.

Determination of the weights of technical criteria influencing the performance of petrol-powered and battery powered chainsaws by means of the Entropy Method

Determination of the weights of technical criteria influencing the performance of petrol-powered and battery powered chainsaws by means of the Entropy Method

Stability of the composite wave of two planar viscous shock waves for the compressible Navier–Stokes system

We are concerned with the nonlinear stability of the composite wave consisting of two planar viscous shock waves to the three-dimensional compressible Navier–Stokes system. It is shown that if the shock strengths are suitably small but not necessarily of the same order of magnitude, and the initial perturbations are suitably small without the zero-mass conditions, then there exists a unique, globally strong solution in time to the compressible Navier–Stokes system, which asymptotically approaches the corresponding composite wave up to time-dependent shifts in L^{\infty} norm. The proof employs the weighted relative entropy method, an L^{2} -contraction technique with time-dependent shifts to the shocks developed by Kang and Vasseur [J. Eur. Math. Soc. (JEMS) 23 (2021), 585–638; Invent. Math. 224 (2021), 55–146]. We perform the stability analysis within the original H^{2} -perturbation framework instead of using the anti-derivative technique. Compared with the previous work of the author and Wang [J. Eur. Math. Soc. (JEMS) (2023), DOI 10.4171/JEMS/1486] for the single shock case, a major difficulty is the construction of shifts to ensure that the two shock waves are well separated.

The spatial correlation of economic institutional change in China and its impact on economic growth: A social network analysis approach.

Economic institutional change is a vital driving force behind the rapid rise of China's economy. However, the incremental approach to economic institutional change has caused unbalanced transformation and economic growth. To this end, we adopted the entropy method to measure the economic institutional change index, and employed social network analysis to reveal its spatial correlation characteristics. We then applied QAP analysis to empirically demonstrate the impact of China's economic institutional change on regional disparities in economic growth. The findings indicated a gradual increase in the level of economic institutions over time and a spatial gradient between the eastern, central, and western regions. Moreover, the spatial correlation network of China's economic institutional change is stable and gradually improving. Nevertheless, the role of provinces in the process of economic institutional change varies: the eastern coastal provinces play a dominant role, the central and western provinces benefit to a lesser extent, and some provinces in northeastern China play a "bridging" and "intermediary" role. Regional differences in China's economic institutional change have widened the regional disparities in China's economic growth, and the impact of each dimension of economic institutions on regional disparities in economic growth is characterized by phases.

Analysis of Spatiotemporal Evolution of Coordinated Development Between Transportation Infrastructure and Ecological Environment in the Yangtze River Economic Belt

The coupling and coordinated development of transportation infrastructure and ecological environment is an important way to achieve win-win economic, social, and ecological benefits. This study analyzes the coupling and coordinated development between transportation infrastructure and ecological environment in the Yangtze River Economic Belt. Based on panel data from 11 provinces in the Yangtze River Economic Belt from 2007 to 2022, establish their respective indicator systems and use entropy method to measure the comprehensive level of the two. Through the perspective of spatiotemporal differentiation, this study analyzes the changes in the coupling and coordinated development level of transportation infrastructure and ecological environment in 11 provinces. It is found that the overall coupling and coordinated development level of each province has significantly improved, but there are obvious regional differences. In the future, each province should formulate more precise and effective policy measures based on its own actual situation, strengthen regional cooperation and communication, and jointly promote the coupling and coordinated development of transportation infrastructure and ecological environment protection in the Yangtze River Economic Belt.

Analysis and study of digital economy level measurement index

PurposeThis study aims to assess the level of development of the digital economy by constructing a comprehensive measurement system. It explores regional differences within China’s digital economy, highlighting the varying degrees of digital infrastructure, industrialization, governance and innovation capabilities across provinces.Design/methodology/approachA multidimensional analytical framework including digital infrastructure, industrialization, digitization, governance and innovation was developed. Entropy methods were used to calculate the weights of each dimension. The coupled coordination degree model and the Tobit model with random effects panel are applied to analyze the current situation, discrepancies and influencing factors.FindingsThis study reveals significant regional differences in the development of China’s digital economy, characterized by a pattern of “strong in the east, weak in the west; high in the south, low in the north.” This geographical imbalance exacerbates the “polarization effect” and the “siphon effect,” where resources and growth tend to concentrate in already developed areas, further intensifying regional inequalities. The development of the digital economy is driven by principles of innovation, coordination and sharing, which facilitate the creation and dissemination of new technologies and collaboration across different sectors. However, this progress is also constrained by considerations of environmental sustainability (green) and economic openness.Originality/valueThis paper contributes to the body of knowledge by providing a novel multidimensional measurement system for the level of digital economy development. The unique application of the coupled coordination degree model and Tobit model to analyze regional differences and influencing factors provides insights into the dynamics of China’s digital economy.

Bearing fault diagnosis based on novel hierarchical multiscale dispersion entropy in corresponding color block images

Abstract The rolling bearing is a critical component of mechanical equipment, and its failure can lead to serious consequences. In order to effectively extract fault features of rolling bearings and improve fault diagnosis performance, a fault diagnosis framework based on hierarchical multiscale dispersion entropy (HMDE) and improved histogram of oriented gradient (HOG) is proposed by combining entropy method with image recognition method. Firstly, the original vibration signal is subjected to moving average filtering to eliminate sudden noise and outliers. Then, HMDE is used for the extraction of fault features. HMDE can evaluate the complexity of the signal at different levels and scales, thereby extracting more comprehensive information. Based on HMDE, entropy color block (ECB) images are generated and the improved HOG of the images are extracted. Finally, Knearest neighbor (KNN) is used to classify the improved HOG features, completing the recognition of different working states of rolling bearings. The validity and robustness of the proposed fault diagnosis framework are proved by the verification experiments on the public bearing datasets in Case Western Reserve University and Southeast University.

Maximum entropy method for valence quark distributions in exotic hadrons: a study of the Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(3900)$$\\end{document} case

In this study we demonstrate the application of the maximum entropy method (MEM) to determine the valence quark distribution of exotic hadrons. Our investigation yields three key findings. Firstly, we observe a significant shift towards smaller Bjorken scale x in the peak position of the valence quark distribution for hadrons with an increasing number of valence quarks, consistent with previous results by Kawamura and Kumano. Secondly, assuming that the Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(3900)$$\\end{document} initially consists of four valence quarks, we employ MEM to determine its initial valence quark distribution, estimating a radius of rc=1.276\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_c=1.276$$\\end{document} fm at an extremely low resolution scale Q2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^2$$\\end{document}. Furthermore, we identify a notable discrepancy between our computed charge form factor Gc(q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_c(q)$$\\end{document} at leading order and the outcomes of hadron molecular state calculations. We propose that this form factor can be extracted from the QCD counting rule cross-section, which is grounded in generalized distribution amplitudes (GDA) linked to the multi-quark states.

Promoting Cultural Industry Management in the Context of a Green Ecological Environment

The green cultural industry is a key driving force for economic transformation and the upgrading of industrial structures. However, to achieve its development while protecting the environment, its influencing factors and the interactive relationship between the economy and the environment must be considered. This paper examines the environmental promotion effect of the green cultural industry by analyzing the interaction mechanism among these three elements, using the entropy method and coupling coordination model. The results show that the green cultural industry can develop cultural resources in line with national cultural characteristics, foster cultural innovation, promote economic growth, and reduce ecological resource consumption. At the same time, economic improvement enhances infrastructure, provides services to support the cultural industry, strengthens environmental protection, and improves ecological carrying capacity, offering greater resource support for cultural industry development.

Pricing and Replenishment Decision System Based on LSTM

Fresh supermarket vegetables have a very short shelf life, and the quality of vegetables will also be affected by the storage time. If most of the goods are not sold on that day, they will not be sold on the next day. From the demand side, the sales volume of vegetables is related to the supply side of vegetables from April to October. At the same time, the sales space of the supermarket is limited, which makes a reasonable sales portfolio extremely important. The commercial overpricing replenishment decision system based on LSTM analyzes the relationship between daily sales volume and cost-plus pricing for each vegetable category and single product over three years. It predicts the sales volume and wholesale price of each category for the next week, determining replenishment volume and pricing strategy based on forecasted sales volume and average loss rate. The system considers limited sales space and uses the entropy method to calculate weights for key indicators like total profit. It employs the TOPSIS method to sort items, considering forecasted wholesale prices, to select items for pricing decisions. The system aims to maximize total profit while ensuring the supermarket meets minimum display conditions. By assisting supermarkets in formulating more reasonable pricing strategies, it aims to reduce overstock, backlog, or stock shortages, ultimately improving sales volume and operational efficiency.

Optimal Capacity Allocation for Life Cycle Multiobjective Integrated Energy Systems Considering Capacity Tariffs and Eco-Indicator 99

Traditional energy systems pose a significant threat to human social development due to fossil fuel depletion and environmental pollution. Integrated energy systems (IESs) are widely studied and applied due to their clean and low-carbon characteristics to achieve sustainable development. However, as integrated energy systems expand, their impact on ecosystems becomes more pronounced. This paper introduces the concept of the ecological damage index (EDI) to promote the sustainable development of integrated energy systems. Moreover, the introduction of a capacity tariff mechanism will impact the energy structure, making it essential to consider its effects on capacity allocation within integrated energy systems. This paper proposes a multiobjective optimization framework for constructing a capacity planning model for integrated energy systems, focusing on achieving a multidimensional balance between the economy, environment, and ecosystem using the life cycle assessment (LCA) method. Finally, the nondominated sorting genetic algorithm-II (NSGA-II) is employed to optimize the three objectives and obtain the Pareto frontier solution set. The optimal solution is selected from the solution set by combining the technique for order preference by similarity to ideal solution (TOPSIS) and Shannon entropy method. In comparison to scenarios with incomplete considerations, the multiobjective capacity optimization model proposed in this study exhibits significant improvements across the three metrics of cost, carbon emissions, and the ecological damage index, with a 19.05% reduction in costs, a 26.24% decrease in carbon emissions, and an 8.85% decrease in the ecological damage index. The study demonstrates that the model abandons traditional single-objective research methods by incorporating a multidimensional balance of the economy, environment, and ecosystems. This approach forms a foundational basis for selecting the optimal energy mix and achieving sustainable development in integrated energy systems. The life cycle assessment methodology evaluates impacts across all stages of integrated energy systems, providing a comprehensive basis for assessing and planning the sustainable development of the systems. The study offers guidance for the rational allocation of the integrated energy system capacity and advances the sustainable development of such systems.

Spatiotemporal Evolution and Influencing Factors of Coupling and Coordination between the Ecosystem Service Value and Economy in the Pearl River Delta Urban Agglomeration of China

In the context of pursuing high-quality development, the coupling and coordination of the ecosystem and economy has become the fundamental goal and inevitable choice for achieving the sustainable development of urban agglomerations. Based on remote sensing and statistical data for the Pearl River Delta (PRD) region from 2005 to 2020, in this paper, we construct an index system of the ecological and economic levels to assess the ecosystem service value (ESV). We use the equivalent factor method, entropy method, coupling coordination model, and relative development model to systematically grasp the spatial pattern of the levels of the two variables, analyse and evaluate their spatial and temporal coupling and coordination characteristics, and test the factors influencing their coupling and coordination using the geographical and temporal weighted regression (GTWR) model. The results show that ① the ESV in the PRD exhibited a fluctuating decreasing trend, while the level of the economy exhibited a fluctuating increasing trend; ② the coordination degree of the ESV and economy in the PRD exhibited a fluctuating increasing trend, and the region began to enter the basic coordination period in 2007; ③ in terms of the spatial distribution of the coordination degree, there was generally a circular pattern, with the Pearl River Estuary cities as the core and a decrease in the value towards the periphery; ④ the coordinated development model is divided into balanced development, economic guidance, and ESV guidance, among which balanced development is the major type; ⑤ the results of the GTWR reveal that the influencing factors exhibited significant spatial–temporal heterogeneity. Government intervention and openness were the dominant factors affecting the coordination, and the normalised difference vegetation index was the main negative influencing factor.

Optimization of ore pillar recovery based on weighting combined with uncertainty measurement theory

Abstract Given the multi-objective nature and inherent uncertainty in evaluating ore pillar mining schemes, the analytic hierarchy process (AHP) and entropy method were applied to determine factor weights. A new combined weighting method was proposed to obtain more objective and accurate results. Seven quantitative and four qualitative indicators were selected based on various mining performance factors and grading standards. A combined weighting–uncertainty measurement theory evaluation model was then constructed, integrating weight values and confidence levels from the recognition criteria. This model was applied to evaluate three proposed schemes, determining their relative merits and ranking. The evaluation demonstrated that the combined weighting–uncertainty measurement model outperformed both the fuzzy theory and the TOPSIS method in delivering comprehensive, objectivity and reliable results for assessing ore pillar mining schemes.

How Can Digital Villages Improve Basic Public Services Delivery in Rural Areas? Evidence from 1840 Counties in China

Digital transformation is spreading from urban to rural areas, and the construction of digital villages has become a key growth point for rural sustainable development globally. Digital villages improve the level of basic public services delivery in rural areas via the penetration of digital technology. However, few studies have empirically investigated the theoretical mechanisms underlying the impact of digital villages on various aspects of rural basic public services. To address these gaps, this study investigates the impact mechanisms of digital villages on rural basic public services delivery in terms of accessibility, equity, agility, holistic nature and participation. Using 1840 counties in China as the research sample, this study applies the entropy method to extract a composite index of basic public services and performs correlation, regression, and heterogeneity analyses to examine the effects of digital villages on basic public services delivery. Empirical analysis results show that the construction of digital villages is positively associated with the level of basic public services in rural areas. Meanwhile, heterogeneity analysis results confirms that this relationship is mainly observed in eastern counties but not observed in central and western counties. These findings provide a basis for using digital inclusion to improve basic public services delivery in rural areas and achieve balanced development across regions.

Maximum Entropy Methods for Quantum State Compatibility Problems

Maximum Entropy Methods for Quantum State Compatibility Problems