Entropy最新文献

Multi-stable behavior at the microscopic length-scale is fundamental for phase transformation phenomena observed in many materials. These phenomena can be driven not only by external mechanical forces but are also crucially influenced by disorder and thermal fluctuations. Disorder, arising from structural defects or fluctuations in external stimuli, disrupts the homogeneity of the material and can significantly alter the system's response, often leading to the suppression of cooperativity in the phase transition. Temperature can further introduce novel effects, modifying energy barriers and transition rates. The study of the effects of fluctuations requires the use of a framework that naturally incorporates the interaction of the system with the environment, such as Statistical Mechanics to account for the role of temperature. In the case of complex phenomena induced by disorder, advanced methods such as the replica method (to derive analytical formulas) or refined numerical methods based, for instance, on Monte Carlo techniques, may be needed. In particular, employing models that incorporate the main features of the physical system under investigation and allow for analytical results that can be compared with experimental data is of paramount importance for describing many realistic physical phenomena, which are often studied while neglecting the critical effect of randomness or by utilizing numerical techniques. Additionally, it is fundamental to efficiently derive the macroscopic material behavior from microscale properties, rather than relying solely on phenomenological approaches. In this perspective, we focus on a paradigmatic model that includes both nearest-neighbor interactions with multi-stable (elastic) energy terms and linear long-range interactions, capable of ensuring the presence of an ordered phase. Specifically, to study the effect of environmental noise on the control of the system, we include random fluctuation in external forces. We numerically analyze, on a small-size system, how the interplay of temperature and disorder can significantly alter the system's phase transition behavior. Moreover, by mapping the model onto a modified version of the Random Field Ising Model, we utilize the replica method approach in the thermodynamic limit to justify the numerical results through analytical insights.

It is customary to classify approaches in statistical mechanics (SM) as belonging either to Boltzmanninan SM (BSM) or Gibbsian SM (GSM). It is, however, unclear how the Boltzmann equation (BE) fits into either of these approaches. To discuss the relation between BE and BSM, we first present a version of BSM that differs from standard presentation in that it uses local field variables to individuate macro-states, and we then show that BE is a special case of BSM thus understood. To discuss the relation between BE and GSM, we focus on the BBGKY hierarchy and note the version of the BE that follows from the hierarchy is "Gibbsian" only in the minimal sense that it operates with an invariant measure on the state space of the full system.

In this paper, by using eleven entangled quantum states as a quantum channel, we propose a cyclic and asymmetric novel protocol for four participants in which both Alice and Bob can transmit two-qubit states, and Charlie can transmit three-qubit states with the assistance of the supervisor David, who provides a guarantee for communication security. This protocol is based on GHZ state measurement (GHZ), single-qubit measurement (SM), and unitary operations (UO) to implement the communication task. The analysis demonstrates that the success probability of the proposed protocol can reach 100%. Furthermore, considering that in actual production environments, it is difficult to avoid the occurrence of noise in quantum channels, this paper also analyzes the changes in fidelity in four types of noisy scenarios: bit-flip noise, phase-flip noise, bit-phase-flip noise, and depolarizing noise. Showing that communication quality only depends on the amplitude parameters of the initial state and decoherence rate. Additionally, we give a comparison with previous similar schemes in terms of achieved method and intrinsic efficiency, which illustrates the superiority of our protocol. Finally, in response to the vulnerability of quantum channels to external attacks, a security analysis was conducted, and corresponding defensive measures were proposed.

We discuss a family of W-class states describing three-qubit systems. For such systems, we analyze the relations between the entanglement measures and the nonlocality parameter for a two-mode mixed state related to the two-qubit subsystem. We find the conditions determining the boundary values of the negativity, parameterized by concurrence, for violating the Bell-CHSH inequality. Additionally, we derive the value ranges of the mixedness measure, parameterized by concurrence and negativity for the qubit-qubit mixed state, guaranteeing the violation and non-violation of the Bell-CHSH inequality.

A fractal-order entropy dynamics model is developed to create a modified form of Maxwell's time-dependent electromagnetic equations. The approach uses an information-theoretic method by combining Shannon's entropy with fractional moment constraints in time and space. Optimization of the cost function leads to a time-dependent Bayesian posterior density that is used to homogenize the electromagnetic fields. Self-consistency between maximizing entropy, inference of Bayesian posterior densities, and a fractal-order version of Maxwell's equations are developed. We first give a set of relationships for fractal derivative definitions and their relationship to divergence, curl, and Laplacian operators. The fractal-order entropy dynamic framework is then introduced to infer the Bayesian posterior and its application to modeling homogenized electromagnetic fields in solids. The results provide a methodology to help understand complexity from limited electromagnetic data using maximum entropy by formulating a fractal form of Maxwell's electromagnetic equations.

We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of ϵ-machines. We characterize ϵ-machines in the language of automata theory and adapt a recent algorithm for generating accessible deterministic finite automata, pruning this over-large class down to that of ϵ-machines. As an application, we exactly enumerate topological ϵ-machines up to eight states and six-letter alphabets.

Maximum correntropy criterion (MCC) has been an important method in machine learning and signal processing communities since it was successfully applied in various non-Gaussian noise scenarios. In comparison with the classical least squares method (LS), which takes only the second-order moment of models into consideration and belongs to the convex optimization problem, MCC captures the high-order information of models that play crucial roles in robust learning, which is usually accompanied by solving the non-convexity optimization problems. As we know, the theoretical research on convex optimizations has made significant achievements, while theoretical understandings of non-convex optimization are still far from mature. Motivated by the popularity of the stochastic gradient descent (SGD) for solving nonconvex problems, this paper considers SGD applied to the kernel version of MCC, which has been shown to be robust to outliers and non-Gaussian data in nonlinear structure models. As the existing theoretical results for the SGD algorithm applied to the kernel MCC are not well established, we present the rigorous analysis for the convergence behaviors and provide explicit convergence rates under some standard conditions. Our work can fill the gap between optimization process and convergence during the iterations: the iterates need to converge to the global minimizer while the obtained estimator cannot ensure the global optimality in the learning process.

Federated learning enables devices to train models collaboratively while protecting data privacy. However, the computing power, memory, and communication capabilities of IoT devices are limited, making it difficult to train large-scale models on these devices. To train large models on resource-constrained devices, federated split learning allows for parallel training of multiple devices by dividing the model into different devices. However, under this framework, the client is heavily dependent on the server's computing resources, and a large number of model parameters must be transmitted during communication, which leads to low training efficiency. In addition, due to the heterogeneous distribution among clients, it is difficult for the trained global model to apply to all clients. To address these challenges, this paper designs a sparse gradient collaborative federated learning model for heterogeneous data on resource-constrained devices. First, the sparse gradient strategy is designed by introducing the position Mask to reduce the traffic. To minimize accuracy loss, the dequantization strategy is applied to restore the original dense gradient tensor. Second, the influence of each client on the global model is measured by Euclidean distance, and based on this, the aggregation weight is assigned to each client, and an adaptive weight strategy is developed. Finally, the sparse gradient quantization method is combined with an adaptive weighting strategy, and a collaborative federated learning algorithm is designed for heterogeneous data distribution. Extensive experiments demonstrate that the proposed algorithm achieves high classification efficiency, effectively addressing the challenges posed by data heterogeneity.

We present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel-Young inequality which relies on the notion of symplectic subdifferentials. The symplectic Fenchel-Young inequality is obtained using the symplectic Fenchel transform which is defined with respect to the symplectic form. Since symplectic forms can be built generically from pairings of dual systems, we obtain a generalization of Bregman divergences in dual systems obtained by equivalent symplectic Bregman divergences. In particular, when the symplectic form is derived from an inner product, we show that the corresponding symplectic Bregman divergences amount to ordinary Bregman divergences with respect to composite inner products. Some potential applications of symplectic divergences in geometric mechanics, information geometry, and learning dynamics in machine learning are touched upon.

We develop a novel key routing algorithm for quantum key distribution (QKD) networks that utilizes a distribution of keys between remote nodes, i.e., not directly connected by a QKD link, through multiple non-overlapping paths. This approach focuses on the security of a QKD network by minimizing potential vulnerabilities associated with individual trusted nodes. The algorithm ensures a balanced allocation of the workload across the QKD network links, while aiming for the target key generation rate between directly connected and remote nodes. We present the results of testing the algorithm on two QKD network models consisting of 6 and 10 nodes. The testing demonstrates the ability of the algorithm to distribute secure keys among the nodes of the network in an all-to-all manner, ensuring that the information-theoretic security of the keys between remote nodes is maintained even when one of the trusted nodes is compromised. These results highlight the potential of the algorithm to improve the performance of QKD networks.