Entropy最新文献

Complex systems-ranging from biological organisms to turbulent fluids-exhibit multiscale heterogeneity and intermittency that traditional, differentiable calculus fails to adequately capture. Therefore, we propose a mathematical framework for analyzing complex system dynamics by assimilating the trajectories of structural units to continuous but non-differentiable multifractal curves. Utilizing the scale covariance principle, the authors recast the conservation of momentum as a geodesic equation within a multifractal space. This approach naturally separates the complex velocity field into differentiable and non-differentiable scale resolutions, where the balance of multifractal acceleration, convection, and dissipation is parametrized by a singularity spectrum f(α). We also discuss broad interdisciplinary implications, because, in our opinion, non-differentiability can enhance predictive capabilities in various fields such as oncology, pharmacology, and geophysics.

We study the pinning transition in a (1+1)-dimensional lattice model of a fluctuating interface interacting with a corrugated impenetrable wall. The interface is modeled as an N-step directed one-dimensional random walk on the half-line x≥0. Its interaction with the wall is described by a quenched, site-dependent, short-ranged random potential uj (j=1,…,N), distributed according to Q(uj) and localized at x=0. By computing the first two disorder-averaged moments of the partition function, ⟨GN⟩ and ⟨GN2⟩, and by analyzing the analytic structure of the resulting expressions, we derive an explicit criterion for the coincidence or distinction of the pinning transitions in annealed and quenched systems. We show that, although the transition points of the annealed and quenched systems are always different in the thermodynamic limit, for finite systems there exists a "gray zone" in which this difference is hardly detectable. Our results may help reconcile conflicting views on whether quenched disorder is marginally relevant.

The computational complexity, or quantum advantage, of Gaussian boson sampling is ascribed to squeezing of the Wigner quasiprobability distribution. This approach reveals the physical origin of the quantum complexity resource. This approach sets an easy-to-compute universal lower bound for the complexity dimension determined by the boson number in the quantum complexity resource. It is shown that the Wigner lower bound is close to the exact value of the complexity dimension obtained via numerical convex optimization. Our analytical and numerical results disclose a series of remarkable properties of quantum advantage.

An attosecond optical pulse can entangle coherently related states of different characters, such as electronic and vibrational, in a molecular system. Using a quantum information theoretic approach, we explicitly define and discuss the surprisal of such a system in the maximal entropy formalism and identify the constraints and their conjugate Lagrange multipliers. Surprisal analysis shows how these constraints become fewer and simpler in the sudden approximation of the dynamics, a limit often valid for an ultrafast excitation. The optically accessible lower electronic states of N₂ are used as a numerical example to show the compaction of the dynamics from On2 down to On constraints, where n is the number of vibronic states. The von Neumann entropy is used to confirm the fidelity of the compaction.

Uncovering latent structures from complex, degraded data is a central challenge in modern unsupervised learning, with critical implications for downstream tasks. This principle is exemplified in the domain of aerial imagery, where the quality of images captured by drones is often compromised by complex, flight-induced degradations, thereby raising the information entropy and obscuring essential semantic patterns. Conventional super-resolution methods, trained on generic data, fail to restore these unique artifacts, thereby limiting their effectiveness for vessel identification, a task that fundamentally relies on clear pattern recognition. To bridge this gap, we introduce a novel adaptive super-resolution framework for ship images captured by drones. The approach integrates a static stage for foundational feature extraction and a dynamic stage for adaptive scene reconstruction, enabling robust performance in complex aerial environments. Furthermore, to ensure the super-resolution model's generalizability and effectiveness, we optimize the design of degradation methods based on the characteristics of drone aerial images and construct a high-resolution dataset of ship images captured by drones. Extensive experiments demonstrate that our method surpasses existing state-of-the-art algorithms, confirming the efficacy of our proposed model and dataset.

Mathematical and computational models, which have been successfully used in various fields of biology, are particularly relevant in studies on the origin of life, where wet experiments have not yet been able to obtain fully "living" entities from abiotic materials. This paper investigates mathematical and computational models of interacting polymers in prebiotic environments to understand how molecular replication and protocell reproduction could emerge. This study builds on the Binary Polymer Model (K-BPM), in which polymers are represented as binary strings that undergo catalyzed condensation and cleavage reactions, by introducing a biologically relevant variant (C-BPM), where catalytic activity depends on polymer structure. The model is analyzed with respect to the formation of autocatalytic networks, formalized as Reflexive Autocatalytic Food-generated (RAF) sets, embedded in a protocell in order to simulate their dynamics. The results show clear differences between K-BPM and C-BPM models. They also show that the existence of a RAF does not guarantee the survival of a population of protocells, although it may be possible when only a subset of the existing species partakes in the RAF, thus suggesting that small autocatalytic networks may have preceded the larger networks found in modern life.

Water quality monitoring is critical for public health, ecology, and economic sustainability, but traditional methods are limited by temporal-spatial coverage and cost, failing to meet real-time assessment needs. Deep learning for water quality prediction is often hindered by high complexity and noise in raw time series. This study aims to address the high complexity and noise of hydrological time series by proposing a prediction framework integrating sliding window feature enhancement, principal component analysis (PCA), and a two-layer regularized gated recurrent unit (TLR-GRU). The core goal is to achieve high-precision real-time prediction of four key water quality parameters (dissolved oxygen (DO), ammonia nitrogen (NH3-N), total phosphorus (TP), and total nitrogen (TN)) for aquaculture and irrigation. Sample entropy (SampEn, m=2, r=0.2 × std(X)), a univariate complexity metric capturing intra-series pattern repetition, quantifies time series regularity, showing sliding windows reduce SampEn by filtering transient noise while retaining ecological patterns. This optimization synergizes with TLR-GRU's regularization (L2, Dropout) to avoid overfitting. A total of 4970 water quality records (2020-2023, 4 h sampling interval) were collected from a monitoring station in a typical aquaculture-irrigated water body. After dimensionality reduction via PCA, experimental results demonstrate that the TLR-GRU model outperforms six state-of-the-art deep learning models (e.g., TLD-LSTM, WaveNet) on both the base dataset and the sliding window-enhanced dataset. On the latter, DO and TP test set R2 rise from 0.82 to 0.93 and 0.81 to 0.92, with RMSE decreasing by 49.4% and 55.6%, respectively. This framework supports water resource management, applicable to rivers and lakes beyond aquaculture. Future work will optimize the model and integrate multi-source data.

Wireless sensor networks (WSNs) are extensively used in IoT applications. Secure access control and data protection are essential. Nonetheless, the wireless environment has an open nature. The limited resources of sensor devices render WSNs susceptible to a variety of security attacks, causing significant difficulties in the design phase of efficient authentication and key agreement (AKA) protocols. This study proposes a physically unclonable function (PUF)-based lightweight and secure AKA protocol for WSNs based on elliptic curve cryptography (ECC). A secure password update scheme is offered, which would allow legitimate users to reset forgotten passwords without re-registration. According to formal security analysis using BAN logic and ProVerif, the proposed protocol is secure against common attacks. Moreover, from an entropy perspective, the use of dynamic pseudonyms and fresh session randomness increase an adversary's uncertainty about user identities, thereby limiting identity-related information leakage. Performance evaluation shows that the proposed protocol achieves lower computational and communication overhead than the existing ones, making it suitable for WSNs with resource constraints.

In today's information ecosystem, disinformation threatens civic autonomy and the stability of public discourse. Beyond the intentional spread of false information, it often appears as narrative divergence among sources interpreting shared events, generating fragmentation and measurable losses in structural coherence. This study examines disinformation within an entropic structural framework, defining it as narrative disorder and epistemic incoherence in information systems. The approach moves beyond fact-checking by treating narrative structure and informational order as quantifiable attributes of public communication. We present the QVP-RI (Relational Information Valuation) operator, a computational model that quantifies narrative divergence through informational entropy and normalized structural divergence, without issuing truth assessments. Implemented through state-of-the-art NLP pipelines and entropic analysis, the operator maps narrative structure and epistemic order across plural media environments. Unlike accuracy-driven approaches, it evaluates narrative coherence and informational utility (IU) as complementary indicators of epistemic value. Experimental validation with 500 participants confirms the robustness of the structural-entropic model and identifies high divergence regions, revealing communication vulnerabilities and showing how narrative disorder enables disinformation dynamics. The QVP-RI operator thus offers a computationally grounded tool for analyzing disinformation as narrative divergence and for strengthening epistemic order in open information systems.

Railway passenger flow forecasting plays a critical role in operational efficiency and resource allocation for transportation systems. However, existing deep learning approaches suffer significant performance degradation when facing rare but high-impact events, primarily due to sample scarcity and their inability to distinguish between routine patterns and disruption regimes. To address these challenges, this study introduces EA-ARIMA-Informer, an adaptive forecasting framework that integrates entropy-augmented ARIMA with Informer through an entropy-guided regime-switching mechanism. The passenger flow series is characterized through a multi-dimensional entropy space comprising four complementary measures: Sample Entropy quantifies local regularity and predictability, Permutation Entropy captures the complexity of ordinal dynamics, Transfer Entropy measures causal information flow from external events (holidays, weather) to passenger demand, and the Conditional Entropy Growth Factor (CEGF)-a novel metric introduced herein-detects regime transitions by tracking the rate of uncertainty change between consecutive time windows. These entropy indicators serve dual roles as feature inputs for representation learning and as state identifiers for segmenting the time series into stable and fluctuating regimes with distinct predictability properties. An adaptive dual-path architecture is then designed accordingly: EA-ARIMA handles low-entropy stable regimes where linear seasonality dominates, while EA-Informer processes high-entropy fluctuating regimes requiring nonlinear residual modeling, with CEGF-guided gating dynamically controlling component weights. Unlike conventional black-box gating mechanisms, this entropy-based switching provides physically interpretable signals that explain when and why different model components dominate the forecast. The framework is validated on a large-scale dataset covering nearly 300 Chinese cities over three years (2017-2019), encompassing normal operations, holiday peaks, and extreme weather disruptions. Experimental results demonstrate that EA-ARIMA-Informer achieves a MAPE of 4.39% for large-scale cities and 7.82% for data-scarce small cities (Tier-3), substantially outperforming standalone ARIMA, XGBoost, and Informer, which yield 15.95%, 13.75%, and 12.87%, respectively, for Tier-3 cities. Ablation studies confirm that both entropy-based feature augmentation and CEGF-guided regime switching contribute significantly to these performance gains, establishing a new paradigm for interpretable and adaptive forecasting in complex transportation systems.