Regularity of SRB Entropy for Geometric Lorenz Attractors

Journal of Statistical Physics - We consider the classical geometric Lorenz attractors, showing that the SRB entropy admits $$\gamma $$ -Hölder continuity for any $$0<\gamma <1$$ .     

On the Continuity of the SRB Entropy for Endomorphisms

We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions, which in particular guarantee the existence of SRB measures, we prove that the entropy of the SRB measure varies continuously with the dynamics. We apply our result to a vast class of non-uniformly expanding maps of a compact manifold and prove the continuity of the entropy of the SRB measure. In particular, we show that the SRB entropy of Viana maps varies continuously with the map.     

Generalized Physical and SRB Measures for Hyperbolic Diffeomorphisms

In this paper we introduce the notion of generalized physical and SRB measures. These measures naturally generalize classical physical and SRB measures to measures which are supported on invariant sets that are not necessarily attractors. We then perform a detailed case study of these measures for hyperbolic Hènon maps. For this class of systems we are able to develop a complete theory about the existence, uniqueness, finiteness, and properties of these natural measures. Moreover, we derive a classification for the existence of a measure of full dimension. We also consider general hyperbolic surface diffeomorphisms and discuss possible extensions of, as well as the differences to, the results for Hènon maps. Finally, we study the regular dependence of the dimension of the generalized physical/SRB measure on the diffeomorphism. For the proofs we apply various techniques from smooth ergodic theory including the thermodynamic formalism. 2000 Mathematics Subject Classification. Primary: 37C45, 37D20, 37D35, Secondary: 37A35, 37E30     

Statistical Stability and Continuity of SRB Entropy for Systems with Gibbs-Markov Structures

We present conditions on families of diffeomorphisms that guarantee statistical stability and SRB entropy continuity. They rely on the existence of horseshoe-like sets with infinitely many branches and variable return times. As an application we consider the family of Hénon maps within the set of Benedicks-Carleson parameters.     

SRB Measures for Polygonal Billiards with Contracting Reflection Laws

We prove that polygonal billiards with contracting reflection laws exhibit hyperbolic attractors with countably many ergodic SRB measures. These measures are robust under small perturbations of the reflection law, and the tables for which they exist form a generic set in the space of all convex polygons. Specific polygonal tables are studied in detail.     

Non-Stationary Non-Uniform Hyperbolicity: SRB Measures for Dissipative Maps

We prove the existence of SRB measures for diffeomorphisms where a positive volume set of initial conditions satisfy an “effective hyperbolicity” condition that guarantees certain recurrence conditions on the iterates of Lebesgue measure. We give examples of systems that do not admit a dominated splitting but can be shown to have SRB measures using our methods.     

一类块三对角矩阵求逆的算法

讨论了一类块三对角矩阵的求逆问题.由块三对角矩阵的LU分解,得到了其逆矩阵块元素的显式表达式.当考虑该表达式的结构特征时,可得到块元素的递推关系式,由此得到一个求逆矩阵的新算法.该算法比已有的块三对角矩阵求逆算法的计算复杂度和计算时间低.     

An Evaluation of Entropy Measures for Microphone Identification

Research findings have shown that microphones can be uniquely identified by audio recordings since physical features of the microphone components leave repeatable and distinguishable traces on the audio stream. This property can be exploited in security applications to perform the identification of a mobile phone through the built-in microphone. The problem is to determine an accurate but also efficient representation of the physical characteristics, which is not known a priori. Usually there is a trade-off between the identification accuracy and the time requested to perform the classification. Various approaches have been used in literature to deal with it, ranging from the application of handcrafted statistical features to the recent application of deep learning techniques. This paper evaluates the application of different entropy measures (Shannon Entropy, Permutation Entropy, Dispersion Entropy, Approximate Entropy, Sample Entropy, and Fuzzy Entropy) and their suitability for microphone classification. The analysis is validated against an experimental dataset of built-in microphones of 34 mobile phones, stimulated by three different audio signals. The findings show that selected entropy measures can provide a very high identification accuracy in comparison to other statistical features and that they can be robust against the presence of noise. This paper performs an extensive analysis based on filter features selection methods to identify the most discriminating entropy measures and the related hyper-parameters (e.g., embedding dimension). Results on the trade-off between accuracy and classification time are also presented.     

拉格朗日方法中减小非物理熵增的方法

为了减少Godunov方法在计算等熵流动问题时的非物理现象, 研究单元中心型拉格朗日方法的离散熵增问题。通过对传统数值方法进行压力修正, 提出一种基于完全离散熵不等式的通量修正方法。数值实验表明: 改进后的通量算法在计算包含膨胀波的问题时能够有效地减少原拉格朗日方法的非物理误差。     

Positivity of Entropy Production

We discuss the positivity of the mean entropy production for stochastic systems driven from equilibrium, as it was defined in refs. 7 and 8. Non-zero entropy production is closely linked with violation of the detailed balance condition. This connection is rigorously obtained for spinflip dynamics. We remark that the positivity of entropy production depends on the choice of time-reversal transformation, hence on the choice of the dynamical variables in the system of interest.     

Multiple Entropy Measures for Multi-particle Pure Quantum State

We propose to use a set of averaged entropies, the multiple entropymeasures (MEMS), to partially quantify quantum entanglement ofmultipartite quantum state. The MEMS is vector-like with m=[N/2]components: [S₁, S₂,..., S_m], and the $i$-th component S_i is the geometric mean of i-qubits partial entropy of the system. The S_i measures how strong an arbitrary i qubits from the system are correlated with the rest of the system. It satisfies the conditions for a good entanglement measure. We have analyzed the entanglement properties of the GHZ-state, the W-states, and cluster-states under MEMS.     

Multiple Entropy Measures for Multi-particle Pure Quantum Statet

We propose to use a set of averaged entropies, the multiple entropy measures （MEMS）, to partially quantify quantum entanglement of multipartite quantum state. The MEMS is vector-like with m = [N/2] components： [S1, S2,..., Sm], and the i-th component Si is the geometric mean of i-qubits partial entropy of the system. The Si measures how strong an arbitrary i qubits from the system are correlated with the rest of the system. It satisfies the conditions for a good entanglement measure. We have analyzed the entanglement properties of the GHZ-state, the W-states, and cluster-states under MEMS.     

Expressions for Entropy Production Rate of Fuel Cells

基于燃料电池的一般模型,应用电化学和热力学理论导出燃料电池系统在不同条件下熵产生率的表示式．为了分析存在实际燃料电池中不可逆损失的影响,引进燃料电池的等效电路,直接将燃料电池的不可逆因子表示为内电阻、漏电阻和负载电阻的函数．进而计算燃料电池的最大输出功率和效率,讨论燃料电池的优化运行,确定负载电阻的匹配条件,从而得到一些有意义的结果．     

Gravitational Spin Entropy Production

Spin entropy production for particles with arbitrary spin moving in a curved spacetime is discussed. There is a Wigner rotation due to both the acceleration an the curvature, which causes an initial pure state to transform into a final mixed state. Depending on the spacetime characteristics, one may find paths on which there is no Wigner rotation and the state remains pure.     

Physical Measures for Multivalued Inverse Iterates Near Hyperbolic Repellors

We study new invariant probability measures, describing the distribution of multivalued inverse iterates (i.e. of different local inverse iterates) for a non-invertible smooth function f which is hyperbolic, but not necessarily expanding on a repellor Λ. The methods for the higher dimensional non-expanding and non-invertible case are different than the ones for diffeomorphisms, due to the lack of a nice unstable foliation (local unstable manifolds depend on prehistories and may intersect each other, both in Λ and outside Λ), and the fact that Markov partitions may not exist on Λ. We obtain that for Lebesgue almost all points z in a neighbourhood V of Λ, the normalized averages of Dirac measures on the consecutive preimage sets of z converge weakly to an equilibrium measure μ ⁻ on Λ; this implies that μ ⁻ is a physical measure for the local inverse iterates of f. It turns out that μ ⁻ is an inverse SRB measure in the sense that it is the only invariant measure satisfying a Pesin type formula for the negative Lyapunov exponents. Also we show that μ ⁻ has absolutely continuous conditional measures on local stable manifolds, by using the above convergence of measures. We prove then that f:(Λ,ℬ(Λ),μ ⁻)→(Λ,ℬ(Λ),μ ⁻) cannot be one-sided Bernoulli, although it is an exact endomorphism of Lebesgue spaces. Several classes of examples of hyperbolic non-invertible and non-expanding repellors, with their inverse SRB measures, are given in the end.