Against the backdrop of the rapid development of new quality productive forces, technological progress profoundly reshaped income distribution patterns and consumption structures. On the basis of task-oriented model theory, this paper constructs an analytical chain of technological progress → employment polarization → consumption stratification using panel data from 30 Chinese provinces from 2008--2023. This study innovatively constructs a consumption entropy reduction index (CERI) to quantify the phenomenon of consumption stratification and identifies transmission mechanisms through an employment polarization index (EPI). The findings reveal that technological progress significantly exacerbates consumption stratification: each 1 percentage point increase in R&D investment intensity leads to an average increase of 0.018 units in the consumption entropy reduction index. Employment polarization plays a crucial mediating role, with technological progress leading to employment polarization through ‘skill-biased’ and ‘task-substitution’ mechanisms, which subsequently reshapes income distribution through wage‒price mechanisms and ultimately transmits to the consumption domain, forming stratification. Further research indicates significant regional heterogeneity in the consumption stratification effects of technological progress, with more pronounced stratification effects in the eastern regions of China than in the central and western regions. This study is the first to construct a complete theoretical framework for how technological progress affects consumption stratification, providing important empirical evidence for coordinating technological innovation with common prosperity objectives.

The hydrophobic effect is a crucial guiding force in biological processes such as protein folding, molecular recognition, and structural stability. The enthalpy-entropy interplay at the hydration shell offers key insights into these phenomena. Although molecular dynamics simulations estimate enthalpy, determining entropic contributions, especially at the single-particle level, remains a challenge. This study calculates the translational (trans) and rotational (rot) entropies of water molecules around amino acids and compares the results with those of existing theoretical studies. By applying a permutation reduction technique to the water molecules in molecular dynamics trajectories and using the quasiharmonic approach, we computed the translational entropy of individual molecules. The rotational entropy was calculated using the angular orientation distribution of individual permuted water molecules. The solvation entropy calculated from individual contributions in our method agrees well with that from thermal integration (TI) and grid inhomogeneous solvation theory (GIST). We analyzed the spatial distribution of water entropy around amino acid backbones and side chains, observing a consistent loss of entropy near backbone atoms across all amino acids. Charged residues were associated with greater reductions in the water entropy compared to uncharged ones. Interestingly, a higher reduction in translational water entropy is observed near positively charged amino acids, whereas negatively charged residues reduce the rotational entropy to a greater extent. In general, the total water entropy loss (trans + rot) exhibits an inverted parabolic dependence on the hydropathy index of the amino acids. This study lays the groundwork for calculating water entropy around full protein surfaces, thereby advancing our understanding of hydration-driven processes in biomolecular systems. It also provides a foundation for exploring entropic behavior in molecular recognition, including protein-drug interactions.

X-ray crystallography remains the gold standard for high-resolution structural biology, yet obtaining diffraction-quality crystals continues to pose a major bottleneck due to inherently low success rates. This review advocates a paradigm shift from probabilistic screening to rational engineering, reframing crystallization as a controllable self-assembly process. We provide a comprehensive overview of strategies that connect fundamental physicochemical principles to practical applications, beginning with contact design, which involves the active engineering of crystal contacts through surface entropy reduction (SER), introduction of electrostatic patches. Complementing these molecular approaches, we discuss physicochemical strategies that exploit heterogeneous nucleation on functionalized surfaces and gold nanoparticles (AuNPs) to lower the energy barrier for crystal formation. We also address scaffold design, utilizing rigid fusion partners and polymer-forming chaperones to promote crystallization even from low-concentration solutions. Furthermore, we highlight principles for controlling the behavior of multi-component complexes, based on our experimental experience. Finally, we examine de novo lattice design, which leverages AI tools such as AlphaFold and RFdiffusion to program crystal lattices from first principles. Together, these strategies establish an integrated workflow that links thermodynamic stability with crystallizability.

Supramolecular deep eutectic solvents (SUPRADESs) as novel biomaterials are attracting increasing attention. However, their application to transdermal drug delivery has not yet been fully explored. This study aimed to investigate the internal mechanism and applicability. First, SUPRADESs composed of six cyclodextrins (CDs) and levulinic acid (Lev) were prepared and characterized. Resveratrol (RES) was used as a model drug. A series of experiments combined with molecular dynamics simulations indicated that SUPRADES remarkably enhanced the solubility of RES compared to only CD and Lev, whose solubilizing ability was contrary to the initial binding strength of the host-guest. The thermodynamic parameters and intermolecular interactions confirmed that the complexation formation in SUPRADES was driven by a favorable enthalpy decrease and a larger unfavorable entropy reduction. When the initial entropy contribution of the host-guest binding was smaller (the weak binding strength), the Gibbs free energy change became smaller in SUPRADES, and the solubilization ability of SUPRADES on drug was further increased. Skin penetration studies showed that, compared to RES/CD complexes, SUPRADES significantly enhanced the penetration and retention of RES in the skin. Thermodynamic calculations and molecular interactions studies revealed that the penetration enhancement was related to the improved skin wettability, the denaturation of the α-helix structure of keratin, and the increased skin hydration. Additionally, SUPRADES enhanced the stability and bioactivity of RES and exhibited low cytotoxicity and skin irritation. Overall, our study reveals the molecular mechanisms of SUPRADES-mediated solubility and permeation enhancement, guides the design of drug-SUPRADES formulations, and extends their pharmaceutical applications.

The Faradarmani Consciousness Field, which is a subset of the Cosmic Consciousness Network, is non-physical in nature. Although its characteristics cannot be identified using quantitative instruments, it is possible to detect its effects through experimental design. In this context, the brain’s response under the influence of this field has been investigated in previous studies, and changes in electrical activity have been recorded. It is hypothesized that information transmitted under the influence of this field leads to observable changes at the brain level. Based on information theory introduced by Shannon, entropy calculation provides a quantitative measure of the information content within the data. Accordingly, this study assessed two types of entropy, Shannon entropy and minimum entropy, based on total absolute power and absolute power across various brainwave frequency bands. It is worth noting that although entropy has been examined in previous studies related to consciousness fields in other contexts, this is the first time it has been applied to brain electrical activity. According to the findings, both Shannon and minimum entropy of total brain activity decreased under the influence of the Faradarmani Consciousness Field, which may serve as a meaningful indicator of its impact on the brain and its electrical activity. From a frequency-based perspective, this entropy reduction, in terms of Shannon entropy, was observed across all frequency bands at the onset of using the Faradarmani Consciousness Field (Task 1), while the reduction in minimum entropy was seen in all bands except high beta and gamma 1.

In this paper, we investigate the thermodynamic behavior of a quantum harmonic oscillator with a positiondependent mass (PDM), where spatial inhomogeneity is introduced through a deformation parameter α. Using the exact energy spectrum, we derive the associated thermodynamic quantities and perform a superstatistical analysis by incorporating fluctuations of the inverse temperature. Within this framework, we examine how mass deformation affects the superstatistical energy distribution and the resulting modified thermodynamic responses. Our results show that increasing α leads to a reduction in entropy and specific heat, reflecting a confinementinduced decrease in the number of accessible microstates. The partition function and free energy display smooth variations across all parameter regimes, indicating the absence of critical phase transitions. Overall, this work highlights the combined effects of mass deformation and superstatistical fluctuations on the thermal behavior of the system and reveals distinctive features that differentiate the PDM oscillator from its constant-mass counterpart.

This paper demonstrates that a designed Boolean logic circuit with feedback connections can transform completely random binary inputs into structured output sequences exhibiting lower Shannonentropy. We establish that the circuit output follows an ergodic Markov chain, which—by the law of large numbers—converges to a non-uniform probability distribution over sequences. This convergence reduces Shannon entropy from its maximum value of 4.7004 bits (for perfectly random sequences) to lower values. We formalize the circuit architecture using combinational logic gates with controlled probabilities and demonstrate through both mathematical derivation and computational experiments that random inputs, when processed through appropriate logic arrangements, can produce increasingly deterministic patterns. This work establishes a fundamental connection between Boolean circuit topology and information-theoretic properties, suggesting that determinism can emerge from randomness through structural design

Abstract As organizations scale, decision velocity often declines due to structural complexity, excessive approval layers, information distortion, and cultural risk aversion. This paper introduces the Leadership Entropy Model (LEM), a conceptual and practical framework explaining why scaling leads to execution slowdown—and how leaders can reverse it. Drawing from 15 interviews across EV manufacturing, construction, IT, gems and jewellery, and HR, the study identifies six entropy drivers: Structural Overload, Excessive Layers, Information Decay, Diffused Accountability, Process Friction, and Risk-Averse Leadership Behaviour. The paper presents the Decision Velocity Equation, demonstrating how velocity deteriorates when inhibitory forces rise faster than clarity, accountability, and information accuracy. Case studies illustrate how entropy silently accumulates and erodes execution capacity. Finally, a three-part framework—Entropy Reduction Interventions, Decision Responsibility Mapping (DRM), and Velocity Governance Blueprint (VGB)—offers leaders actionable pathways to sustain agility, clarity, and responsiveness even at scale. Keywords: Leadership Entropy Model (LEM); Decision Velocity; Organizational Agility; Bureaucracy; Structural Friction; Decision Rights Mapping (DRM)

BackgroundThe association of Alzheimer's risk with patient age suggests a fundamental relationship with entropy. Artificial neural networks learn by changing probabilistic representations called weights, which in brains are the synaptic‐mediated odds of one neuron communicating with another. Changing these synaptic weights takes physical work (W) by the cell, which directly relates to thermodynamic entropy (S) and temperature (T) by the formula dS/dt = (dW/dt)/T. Using a well‐established model of organic neural networks, we apply this relationship to predict selective vulnerability in the brain to age‐associated neurodegeneration.MethodsWe developed two feedforward hierarchical networks with parallel processing pathways at each level to examine the emergent properties of multi‐level information processing. The base layer contained paired input nodes processing randomized inputs (0.4‐0.6 ±0.05), feeding into expanded middle‐layer and top‐layer processing units, representing primary sensory, unimodal, and heteromodal cortices respectively. Model 1 was columnar, and Model 2 was a convergent pyramidal network. For each iteration, we measured the “work” proxies required for weight adjustments, Lyapunov stability, and approximate thermodynamic and informational entropies for a node at each hierarchical level over 2000 iterations.ResultsIn Model 1, the topmost “heteromodal” Layer 3 demonstrated the most significant and variable dynamics. In Lyapunov dynamics analysis, in each cycle Layer 3 starts with the highest variability (0.13 ± 0.08) and ends with stability similar to the other layers (0.00 ± 0.00), indicating substantial stability shifts. For work‐related thermodynamic entropy, in each cycle Layer 3 begins with the highest disorder (0.95 ± 0.18) and shows the largest reduction in entropy over time (AUC: 7.44 ± 1.11). In the informational entropy analysis, Layer 3 starts with lower entropy than the other layers (0.44 ± 0.10) but increases over time to converge on the mean probability of the system input (0.50 ± 0.04). This pattern held for Model 2 as well.ConclusionThe model predicts that heteromodal cortex undergoes more thermodynamic entropy than primary sensory or unimodal cortex over time, suggesting selective vulnerability to age‐related degeneration due to accumulated structural disorder from information processing demands.

Metabolic reprogramming has been implicated as both a cause and consequence of Alzheimer's disease (AD). However, how metabolic signaling dynamics rewire the cellular pathobiology in AD at the single-cell level is still unclear. This gap in knowledge largely limits our understanding of metabolite-sensor responses that underpins AD metabolic heterogeneity and metabolism-based therapeutics development. We present a multi-layered omics framework to characterize genetics-supported metabolite signaling network in specific cellular milieu by integrating large-scale single-cell RNA sequencing, genetics, functional/physical measurements, transcriptomics and metabolomics information. This entails four steps: (1) profiling cell-type-specific metabolic signaling entropies and pathway activities to evaluate the cellular metabolic heterogeneity in patient's brain with AD. (2) proposing a Single Cell FUnctionally MEtabolite-Sensor communication (scFUMES) algorithm for predicting metabolic sensing profiles at single-cell level. (3) Through scFUMES and other omics data, prioritizing AD potential metabolite-sensor communications to inspect metabolic heterogeneity; (4) evaluating phenotype-based metabolic signaling and potential AD targets by comparing brain regions, AD severity, sex difference and APOE4 status. Compared to non-AD, neuronal cells showed a significant reduction in metabolic signaling entropy and pathway activities in middle temporal gyrus (MTG) and dorsolateral prefrontal cortex (DLPFC) in AD, while most of non-neural cells have an opposite trend. Particularly, immune cells showed minimal disorder but elevated metabolic activity. Via scFUMES, we prioritized 410 disease-specific metabolite-sensor pairs significantly enriched in MTG region. For example, we characterized AD-risk FABP3-palmitic acid specific to excitatory neurons and AD-protective FFAR3-butyric acid in Oligodendrocytes. Through Mendelian Randomization analysis, we revealed 27 cell-type specific AD-associated metabolite-sensor pairs in MTG. Specifically, we found that a signaling pair KYAT1-Indole-3-propionic acid (a human gut metabolite), is significantly enriched in excitatory neurons in severe AD. We further identified multiple signaling pairs specific in immune cells, such as VDR-arachidonic acid and ESR1-L-phenylalanine. Moreover, sex differences and APOE4 genotypes also exhibited distinct metabolic dynamics in different brain regions, such as PPARD-glycerol, which is specific in female and non-APOE4 individuals in immune cells. The findings systematically reveal a circulating metabolite-mediated signaling rewiring network, which may shed light on cellular metabolic heterogeneity and cellular metabolism-based therapeutics for AD and other AD-related dementia if broadly applied.

In distributed data environments, classification tasks are challenged by inconsistencies across independently maintained sources. These environments are inherently characterized by high informational uncertainty. Our framework addresses this challenge through a structured process designed for the reduction of entropy in the overall decision-making process. This paper proposes a novel framework that integrates conflict analysis, coalition formation, decision tree induction, and decision template fusion to address these challenges. The method begins by identifying compatible data sources using Pawlak’s conflict model, forming coalitions that aggregate complementary information. Each coalition trains a decision tree classifier, and the final decision is derived through decision templates that fuse probabilistic outputs from all models. The proposed approach is compared with a variant that does not use coalitions, where each local source is modeled independently. Additionally, the framework extends previous work based on decision rules by introducing decision trees, which offer greater modeling flexibility while preserving interpretability. Experimental results on benchmark datasets from the UCI repository demonstrate that the proposed method consistently outperforms both the non-coalition variant and the rule-based version, particularly under moderate data dispersion. The key contributions of this work include the integration of coalition-based modeling with decision trees, the use of decision templates for interpretable fusion, and the demonstration of improved classification performance across diverse scenarios.

Taking entropy theory as a perspective, this paper divides the development of scientific and technological achievements transformation mode into three stages, namely, entropy decreasing structural order, entropy balancing synergy, and entropy increasing value, according to the law of progressive weakening and compensatory substitution. According to the entropy reduction mode from the three dimensions of active empowerment, open system, and intelligence, it explores the role mechanism of scientific and technological achievements transformation in the three aspects of motivation, interests, and obstacles, deduces the nested, iterative, spiral and all-chain scientific and technological achievements transformation modes, and analyzes the domestic scientific and technological achievements to realize the highly efficient transformation and application under the scenario of the fusion of science, education, and industry by taking the Dezhou Park of Qilu University of Technology (Shandong Provincial Academy of Sciences) as an example. The whole-chain fusion model of transformation of scientific and technological achievements achieves optimal allocation of resources, information sharing, and value enhancement among various links under the collaboration of multiple agents, which provides a replicable practical path for the transformation of scientific and technological achievements in other regions and fields.

This paper introduces the UG-EM (Unconditional Gamma-Exponential Model) as a new compound lifetime model designed to enhance flexibility in tail behavior compared to traditional distributions. The UG-EM model provides a unified framework for analyzing deviations from symmetry in survival data, effectively capturing right-skewed patterns, which are commonly observed in real-world lifetime phenomena. The main analytical properties are derived, including the probability density, cumulative distribution, hazard and reversed-hazard functions, mean residual life, and several measures of dispersion and uncertainty. The effects of the UG-EM parameters (α and λ) are examined, showing that increasing either parameter can cause a temporary reduction in entropy H(T) at early times followed by a long-term increase; in some cases, the influence of α is stronger than that of λ. Parameter estimation is carried out using the maximum likelihood method and assessed through Monte Carlo simulations to evaluate estimator bias and variability, highlighting the significant role of sample size in estimation accuracy. The proposed model is applied to three survival datasets (Lung, Veteran, and Kidney) and compared with classical alternatives such as Exponential, Weibull, and Log-normal distributions using standard goodness-of-fit criteria. Results indicate that the UG-EM model offers superior flexibility and can capture patterns that simpler models fail to represent, although the empirical results do not demonstrate a clear, consistent superiority over standard competitors across all tested datasets. The paper also discusses identifiability issues, estimation challenges, and practical implications for reliability and medical survival analysis. Recommendations for further theoretical development and broader model comparison are provided.

Interpreting clinical findings is fundamental to diagnosis and care. However, the contribution of individual features to reducing diagnostic uncertainty remains unclear. Information theory's Shannon entropy offers a way to quantify how much a finding narrows diagnostic possibilities. We analyzed 405 symptoms, physical signs, demographic factors, and tests drawn from 23 reviews to calculate entropy reduction from diagnostic tables and compared them to established accuracy measures, including Youden's index and predictive values. Most features yielded modest uncertainty reductions, with nearly half removing less than one-fifth of uncertainty, while a subset of high-performance findings reduced uncertainty by more than 40%. Entropy reduction correlated strongly with Youden's index and positive predictive value. Entropy analysis may enhance evaluation by highlighting features that offer greater informational benefit.

This study presents a new class of halogenated N-phenylpiperazine and 2-(piperazin-1-yl)pyrimidine derivatives as guests for cucurbit[7]uril (CB[7]), expanding the space of CB[7]-binding ligands. Combining isothermal titration calorimetry (ITC), X-ray crystallography, and computation (attach–pull–release, APR; symmetry-adapted perturbation theory, SAPT), we quantify how halogen identity and position modulate host–guest binding. We find that halogenation provides two position-specific levers for tuning affinity. At the ortho position, both F and Cl enhance dispersion (Cl more strongly), while ortho-F additionally confers pre-organization (intramolecular C–H⋯F) that reduces the entropic penalty. Across the series, the lowest free energies of binding (ΔG) are observed for ligands with ortho-F, consistent with entropy reduction via pre-organization. By contrast, para-substituent effects become significant mainly for larger halogens (Br, I), which can engage the carbonyl-lined portal and enhance enthalpic stabilization. These findings provide a rational strategy for optimizing ligand properties via supramolecular recognition, offering new perspectives for host–guest chemistry.

Plastic crystals are promising for thermal management due to their reversible order-disorder phase transitions, but they often face challenges with significant supercooling caused by high energy barriers. We address this challenge by incorporating 0.5 wt % graphene into tris(hydroxymethyl)aminomethane (Tris), resulting in a 38.8 °C supercooling inhibition while boosting enthalpy by 20.8%. The pivotal role of graphene induces "rotational entropy pinning", achieving a 40.3% reduction in entropy alongside a simultaneous enthalpy increase. This effect is rooted in directional rotation confinement and cooperative hydrogen-bond lattice reconstruction. Employing synchrotron XRD, femtosecond IR spectroscopy, and MD simulations, we capture structural transformations from femtosecond molecular vibrations to macroscopic lattice reorganization. This advancement circumvents the classical trade-off between nucleation efficiency and energy storage capacity, extending its universality to plastic crystalline systems and even solid-liquid phase-change architectures. These insights propose an interface-confined rotational dynamics model, heralding a leap in designing ultralow-hysteresis, high-energy-density materials. This dual role of graphene as both a nucleation promoter and molecular ordering template, validated in other plastic crystal systems, provides a universal strategy to suppress supercooling while enhancing energy storage, which advances plastic crystals toward efficient solid-state thermal regulation.

Abstract We find that the density operator of the nonequilibrium steady state (NESS) of XXZ spin chains with strong ‘sink and source’ boundary dissipation, can be described in terms of quasiparticles, with renormalized—dissipatively dressed—dispersion relation. The spectrum of the NESS is then fully accounted for by Bethe ansatz equations for an associated coherent system of these quasiparticles. The dissipative dressing generates an extra singularity in the dispersion relation, which significantly changes the NESS spectrum. In particular, it leads to a dissipation-assisted entropy reduction, due to the suppression in the NESS spectrum of plain wave-type Bethe states in favor of Bethe states localized at the boundaries.

Entropy inherently tends to increase in the absence of external influence, leading to greater disorder. Herein, the anomalous spontaneous entropy reduction phenomenon was found, as demonstrated by the spontaneous aggregation of floating oil. Specifically, the polytetrafluoroethylene (PTFE) film after laser treating (LT-PTFE) possesses superhydrophobic (a water contact angle of ∼153.5°) and superoleophobic (an oil contact angle of ∼152.0°) properties. Once floating oil came into contact with the LT-PTFE surface, it was adsorbed and spread on it. Ultimately, the oil and water completely separated, achieving floating oil spontaneously aggregated into spherical shapes. We conducted a comprehensive analysis of the critical parameters influencing the movement of both floating oil and water, including floating oil volume, water film thickness, and substrate surface characteristics. Through theoretical calculations and fluid dynamics simulations, the factors essential for the manifestation of this phenomenon were elucidated. We posit that this discovery represents a significant advancement in spontaneous entropy reduction behavior and offers innovative insights into integrating entropy reduction with experimental approaches.

How organisms decrease their entropy.

Tourism uniqueness: Entropy reduction through volitional system switching