Entropy最新文献

In the digital economy, social media has become a critical channel through which corporate executives communicate with investors, thereby influencing market expectations and price dynamics. This study examines how CEO social media behavior affects stock price volatility from an information-theoretic perspective combined with deep learning methods. Using Lei Jun (Xiaomi) and Elon Musk (Tesla) as contrasting cases, we analyze executive communication under transactional and transformational leadership styles. Emotional tone, thematic alignment, and diffusion intensity are extracted using BERT and LDA, and incorporated into a Long Short-Term Memory (LSTM) model to forecast short-term stock price movements. To interpret the mechanism behind the predictive results, we introduce a novel metric: Semantic Resonance Dissipation Entropy (SRE). Derived from Kullback-Leibler divergence, this indicator measures the informational friction between executive semantic output and market attention. The empirical analysis shows that incorporating these high-dimensional semantic features significantly improves volatility prediction. Moreover, leadership style is closely associated with distinct entropic regimes: Transactional leadership corresponds to relatively stable semantic patterns and low entropy, whereas transformational leadership is associated with higher entropy and greater semantic dispersion. Following Musk's acquisition of Twitter, the previously unstable information environment evolved into a persistent structural factor priced by the market. These findings suggest that the economic impact of digital leadership depends on limiting information dissipation to ensure signal clarity in financial markets.

We investigate the entropic consequences of the relaxation of an open two-level quantum system towards a thermalised statistical state, using a framework of quantum state diffusion with evolution described by a minimal set of raising and lowering Lindblad operators. We demonstrate that thermalisation is typically accompanied by a persistent non-zero mean rate of change of the environmental component of stochastic entropy production. This thermodynamic signature can be associated with the purification of the reduced density matrix ρ of the randomly evolving state under these dynamics, which may be contrasted with the impurity of the more frequently considered ensemble average of ρ. The system adopts stationary statistics, with zero stochastic entropy production, after a further stage of relaxation once purity has been achieved. We show that apparent pathological mathematical difficulties in the computation of stochastic entropy production emerge in this evolution towards stationarity if ρ is represented using a certain set of coordinates, though these problems can be removed by choosing a different set. We conclude that frameworks for modelling open systems must be carefully selected to provide satisfactory thermodynamic as well as dynamic behaviour.

Bandlimited functions are functions whose Fourier transform is confined to a finite band of frequencies. We generalize this concept to representations other than the Fourier transform and show that this leads to a variety of inequalities in arbitrary representations. Several special cases are considered, including frequency, dilation, and the chirplet transform, among others. Examples are given to illustrate each result. We apply the results to quantum mechanical wave functions and probability distributions. For bounded momentum wave functions, we obtain explicit bounds on the position wave function and its derivatives, as well as bounds on the position probability distribution. We also consider the dual problem in which the position wave function is bounded, as in the case of a particle in a box with an arbitrary wave function, and obtain bounds on the corresponding momentum wave function and momentum probability distribution. The case of wave functions that are sums of a finite number of energy eigenfunctions is also developed, and bounds on the associated probability distributions are obtained. A number of specific examples are considered, including a truncated Gaussian wave function and a quantum bump wave function.

Ion channels in biological membranes can form spatially localized clusters that exhibit cooperative gating behavior. In this mode, the activity of one channel modulates the opening probability of its neighbors. Understanding such inter-channel interactions is key to elucidating the molecular mechanisms underlying electrochemical signaling and advancing channel-targeted pharmacology. In this study, we introduce a simplified stochastic model of multi-channel gating that allows for systematic analysis of cooperative behavior under controlled conditions. Two information-theoretic metrics, i.e., Shannon entropy and Sample Entropy, are applied to simulated multi-channel datasets, including idealized total current traces and dwell-time sequences of cluster states, to quantify inter-channel cooperativity. We show that the entropic measures display a strong dependency on the strength and type of cooperation (non-, positive, or negative cooperation). The proposed entropy-based framework offers a generalizable and quantitative approach for biomedical data analysis, demonstrating effectiveness in interpreting multi-channel recordings and uncovering cooperative mechanisms in ion channel behavior. The underlying mechanisms by which entropy reflects cooperativity are expected to appear in real recordings, where deviations can further aid in characterizing individual channel features in future work.

I introduce a new analytical framework for estimating critical temperatures in interacting many-body systems, focusing on the Ising model. Combining the Bethe cluster setting, the Metropolis update, and the Galam Majority Model developed in sociophysics, I build a two-stroke pumping technique (TSP). Applied to the Ising model in dimensions d=2,3,4, TSP yields values of Tc which are all at an excess of +0.03 from exact estimates. At d=1, the exact value Tc=0 is obtained. In addition, TSP analytically indicates the practical impossibility of reaching full symmetry breaking at T=0. The results are thus found in good agreement with numerical findings while requiring significantly fewer computational resources than Monte Carlo sampling. Calculations are computationally efficient and transparent. The framework is general and can be extended to a broad class of discrete spin models. This positions TSP as an intermediate yet scalable tool for studying cooperative behavior in many-body interacting systems.

In industries, particularly in quality optimization, the trade-off between model bias and variance is inevitable, reflecting the tension between accuracy and uncertainty. Traditional methods often address these aspects separately, potentially leading to suboptimal decisions. This study proposes a Pareto-front optimization framework for a variance-added expected loss function within the context of interrelated quality characteristics. By integrating multivariate quadratic loss with a variance term, our approach simultaneously captures deviation from targets (bias) and system uncertainty (variance). Unlike sequential approaches that first minimize bias and then variance-often increasing total risk-our weighted formulation flexibly adjusts for their trade-offs. This enables a more balanced and efficient optimization process that identifies solutions with lower overall risk. Through Pareto-front analysis, we reveal trade-offs between expected loss and variance, allowing users to select optimal quality designs based on their preferred bias-variance balance. Representative examples and a case study adopted from the literature validate the effectiveness and practical applicability of the proposed method.

Generative diffusion models have emerged as a powerful class of models in machine learning, yet a unified theoretical understanding of their operation is still developing. This paper provides an integrated perspective on generative diffusion by connecting the information-theoretic, dynamical, and thermodynamic aspects. We demonstrate that the rate of conditional entropy production during generation (i.e., the generative bandwidth) is directly governed by the expected divergence of the score function's vector field. This divergence, in turn, is linked to the branching of trajectories and generative bifurcations, which we characterize as symmetry-breaking phase transitions in the energy landscape. Beyond ensemble averages, we demonstrate that symmetry-breaking decisions are revealed by peaks in the variance of pathwise conditional entropy, capturing heterogeneity in how individual trajectories resolve uncertainty. Together, these results establish generative diffusion as a process of controlled, noise-induced symmetry breaking, in which the score function acts as a dynamic nonlinear filter that regulates both the rate and variability of information flow from noise to data.

Renewable intermittency forces electrolytic hydrogen systems to operate across multiple states, lowering efficiency. We design a thermodynamic cycle that recovers electrolysis waste heat and integrates it with an alkaline electrolyser. A detailed thermodynamic model of the hydrogen system and the heat-recovery loop is developed, and design and operating parameters are optimized to maximize overall exergy efficiency. To improve economic viability, heat-exchanger structural parameters are co-optimized. We further propose an optimal scheduling method for the heat-recovery system under fluctuating renewable supply. The method employs an interactive optimisation framework cantered on the temperature-efficiency curve of alkaline electrolyser cells, jointly optimizing electrolyser current and working-fluid mass flow to enhance economic performance. A case study using real wind-farm data from Qinghai demonstrates that the proposed system with heat recovery significantly improves performance, increasing hydrogen production by up to 9% under wind scarcity compared to that of the system without heat recovery. These results confirm the practical viability of renewable-driven hydrogen production.

Major depressive disorder (MDD) represents a heterogeneous condition lacking reliable neurobiological biomarkers and a mechanistic understanding. Time-resolved characterization of brain dynamics reveals that mental health is associated with a characteristic dynamical regime, exhibiting spontaneous switching between a repertoire of ghost attractor states forming resting-state networks. Analysing resting-state fMRI data from 848 patients with MDD and 794 healthy controls across 17 sites in China (REST-meta-MDD) using Leading Eigenvector Dynamics Analysis (LEiDA), we found patients with MDD exhibited significantly reduced default mode network (DMN) occupancy (p < 0.001; Hedges' g = -0.51) and increased occipito-parieto-temporal state occupancy (p < 0.001; Hedges' g = 0.42), suggesting compensatory dynamical rebalancing. These findings extend prior observations of DMN disruption in MDD, aligning with the emerging dynamical systems framework for mental health to advance the mechanistic understanding of MDD pathophysiology.

As deep learning models are increasingly embedded as critical components within complex socio-technical systems, understanding and evaluating their systemic robustness against adversarial perturbations has become a fundamental concern for system safety and reliability. Deep neural networks (DNNs) are highly effective in visual recognition tasks but remain vulnerable to adversarial perturbations, which can compromise their reliability in safety-critical applications. Existing attack methods often distribute perturbations uniformly across the input, ignoring the spatial heterogeneity of model sensitivity. In this work, we propose the Spatially Distributed Perturbation Strategy with Smoothed Gradient Sign Method (SD-SGSM), a adversarial attack framework that exploits decision-dependent regions to maximize attack effectiveness while minimizing perceptual distortion. SD-SGSM integrates three key components: (i) decision-dependent domain identification to localize critical features using a deterministic zero-out operator; (ii) spatially adaptive perturbation allocation to concentrate attack energy on sensitive regions while constraining background disturbance; and (iii) gradient smoothing via a hyperbolic tangent transformation to enable fine-grained and continuous perturbation updates. Extensive experiments on CIFAR-10 demonstrate that SD-SGSM achieves near-perfect attack success rates (ASR 99.9%) while substantially reducing ℓ2 distortion and preserving high structural similarity (SSIM 0.947), outperforming both single-step and momentum-based iterative attacks. Ablation studies further confirm that spatial distribution and gradient smoothing act as complementary mechanisms, jointly enhancing attack potency and visual fidelity. These findings underscore the importance of spatially aware, decision-dependent adversarial strategies for system-level robustness assessment and the secure design of AI-enabled systems.