基于改进的符号相对熵的脑电信号时间不可逆性研究

提出了一种新的使用过程的前向概率和后向概率计算符号相对熵, 并利用符号相对熵来估计熵产的方法. 该方法是基于熵增和过程不可逆特性关系的, 同时证明脑电信号具有时间不可逆特性, 而且该不可逆特性可以提供脑电信号的熵增信息. 最后应用该方法对青老年脑电信号进行数值计算及对比, 结果是老年人的平均能量损耗显著高于年轻人, 证明符号相对熵可以作为一个物理过程不可逆程度的度量参数, 这对脑电信号是否处于积极或平衡状态的诊断治疗具有积极的作用.     

基于符号相对熵的心电信号时间不可逆性分析

心电图(ECG)信号的时间不可逆性能够反映出心脏的生理功能和健康状态.从短时ECG信号中探测时间不可逆性特征具有重要的现实意义. 文章提出符号相对熵方法(先进行符号化处理,再分别计算它们的时间不可逆性),研究了从MIT-BIH标准数据库中提取的正常窦性心律(normal sinus rhythm,NSR)、心室纤颤(ventricular fibrillation,VF)、心脏猝死(sudden cardiac death,SCD)三种信号.结果表明,这三种信号的时间不可逆性有所不同:NSR信号的时间不可 关键词： 心电信号 相对熵 时间不可逆性     

Information conservation, entropy increase and statistical irreversibility for an isolated system

We consider statistical irreversibility and its compatibility with reversible dynamics. The role played by the observation is analyzed in detail. It makes our previous proof for the second law of thermodynamics clearer. On this basis, we emphasize the importance and wide applicability of the second law of thermodynamics. A new form of physics with this law substituted by the principle of information conservation is suggested. By the way, we also solve the paradox of Schrödinger cat, and show that the universe will not go to the so-called heat death spontaneously.     

Topological entanglement entropy

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity. We show that - gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.     

Information,irreversibility and statistical equilibrium

The note deals with the role of information and sufficiency in the coarse-grained interpretation of irreversibility and statistical equilibrium.     

Asymptotic manipulations of entanglement can exhibit genuine irreversibility

It is commonly believed that distillation of entanglement can be, in general, irreversible. Perhaps the strongest evidence is constituted by the existence of the bound entangled states. However, even a single example of state exhibiting this irreversibility has not been found so far. We show that for a family of states the process of distillation of entanglement is truly irreversible. These states have a nonzero amount of bound entanglement and, at most, a very small amount of free entanglement.     

Valence bond entanglement entropy

We introduce for SU(2) quantum spin systems the valence bond entanglement entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a valence bond solid state and multiplicative logarithmic corrections for the Néel phase.     

Remarks on entropy and irreversibility in non-hamiltonian systems

Entropy and irreversibility in non-hamiltonian systems are discussed from a fully covariant point of view. The discussion is based on the generalized Liouville equation, the definition of a volume element dV in state space, and a generalized hypothesis of equal a priori probabilities. Systems may be classified as reversible or irreversible according to whether it is or is not possible to define dV so that the flow is globally volume-preserving in state space.     

Non-extensive statistical entropy,quantum groups and quantum entanglement

In this work, we explore a new connection between quantum groups and Tsallis entropy through the energy spectrum of a Hamiltonian with S_Uq(2)$S{U}_q\left(2\right)$ symmetry. Identifying the deformation parameter of the entropy with the parameter of deformation of the associated quantum group, we deduce Tsallis entropy for states related to such a system with S_Uq(2)$S{U}_q\left(2\right)$ symmetry and conducted an investigation of quantum entanglement.     

Quantum entropy production as a measure of irreversibility

We consider conservative quantum evolutions possibly interrupted by macroscopic measurements. When started in a nonequilibrium state, the resulting path-space measure is not time-reversal invariant and the weight of time-reversal breaking equals the exponential of the entropy production. The mean entropy production can then be expressed via a relative entropy on the level of histories. This gives a partial extension of the result for classical systems, that the entropy production is given by the source term of time-reversal breaking in the path-space measure.