负P表示非经典光场的信息熵

G.S.Agarwal and K.Tara发现了一个具有负P表示的非经典光场,而此前发现非经典光场的P表示都是奇异的.本文研究了这类负P表示光场的信息熵随场参数m和平均光子数的关系.结果显示,负P表示的非经典光场的Wehrl熵随着场参数m的增大而减小;而当平均光子数增大时,Wehrl熵亦随其增大而减小.同时本文用数值计算的方法研究了负P表示光场的Shannon熵与平均光子数的关系.发现当场参数m一定时,Shannon熵随着平均光子数的增大反而愈来愈小.以上结果表明,当场参数m一定时,随着平均光子数的增大,负P表示光场的非经典性增强;当平均光子数一定时,随着场参数m的增大,负P表示光场的非经典性亦越来越强.这是因为,当m 趋于零时,该光场则演化为经典的热光场;当平均光子数趋于无穷时,该光场则变为Fock态光场.     

多光子T-C模型中场熵的演化

利用Tavis-Cummings模型研究了耦合二能级原子通过多光子跃迁与相干态光场相互作用系统中场熵的演化规律,讨论了原子间耦合强度和光场初始平均光子数的变化对场熵演化的影响。数值计算结果表明: 场熵的演化受原子间耦合强度和光场初始平均光子数的变化的影响.随光场初始平均光子数的增大,场熵平均值增大。     

运动强度相关耦合J-C模型中的熵交换和纠缠

考虑一个运动的二能级原子与单模热光场强度相关耦合,采用量子约化熵研究原子和场的约化熵变化规律、原子与场的熵交换,用共生纠缠度研究原子与场的纠缠。并借助于数值计算方法,详细分析了在强度相关耦合J-C模型中,原子初态、热光场的平均光子数以及场模结构参数对熵交换和纠缠的影响。结果表明原子与光场的熵交换和纠缠均周期性地演化。选择适当的原子初态,可以使得原子的约化熵和光场的约化熵完全交换,这意味着原子与光场反相关。此外,场模结构参数增加导致熵交换的幅度减小,周期缩短。原子与热光场的纠缠随平均光子数的增加而减弱。     

k光子Jaynes-Cummings模型光场的熵压缩

研究了k光子Jaynes-Cummings模型光场的熵压缩,讨论了光子数k和原子的初始状态对光场熵压缩的影响.结果表明,随光子数k的增大,光场的位置熵压缩愈趋明显,动量熵压缩量减小;当k≥3时,位置熵始终是被压缩的.原子的初态对光场的熵压缩也有一定的影响.     

精确求解级联型三能级原子与单模相干态光场场熵的演化特性

本文利用全量子理论,在非旋波近似下对单模相干态光场与级联型三能级原子相互作用过程中场熵随时间的演化进行了精确求解.数值计算的结果表明：随着初始时刻平均光子数n以及光场与原子的耦合强度u, v的增大,场熵的平均值先增大后减小,因此纠缠度也同样先增大后减小;随着失谐量Δ的增大,场熵的平均值逐渐减小,因此纠缠度也逐渐减小. 关键词： 相干态正交化展开 非旋波近似 场熵     

k光子Jaynes-Cummings模型光场的熵压缩

研究了k光子Jaynes-Cummings模型光场的熵压缩,讨论了光子数k和原子的初始状态对光场熵压缩的影响.结果表明,随光子数k的增大,光场的位置熵压缩愈趋明显,动量熵压缩量减小;当k≥3时,位置熵始终是被压缩的.原子的初态对光场的熵压缩也有一定的影响. 关键词： Jaynes-Cummings模型 熵压缩     

k光子Jaynes-Cummings模型光场的熵压缩

研究了k光子Jaynes-Cummings模型光场的熵压缩，讨论了光子数k和原子的初始状态对光场熵压缩的影响.结果表明，随光子数k的增大，光场的位置熵压缩愈趋明显，动量熵压缩量减小；当k≥3时，位置熵始终是被压缩的.原子的初态对光场的熵压缩也有一定的影响.     

两纠缠原子与光场相互作用系统场熵演化特性

研究了两纠缠原子与相干态光场相互作用系统场熵的时间演化特性,运用全量子力学理论和数值方法,讨论了初始两原子所处的纠缠状态、纠缠度和腔内光场的强弱对场熵的影响.随着光场平均光子数的增加,系统场熵均值和振荡频率增大;光场较弱时,场熵呈现一定的周期性振荡;光场增强后,场熵呈现出周期性的崩塌与回复,且随初始两原子纠缠度的增加,场熵的振幅增大.     

Kerr介质中V型三能级原子与双模奇偶纠缠相干光场相互作用的纠缠特性

运用量子约化熵研究了Kerr介质中V型三能级原子与双模奇偶纠缠相干光场相互作用系统中场熵的演化特性.分析了Kerr介质、失谐量和光场的初始平均光子数对场熵的影响.结果表明:Kerr介质与光场的耦合系数对场熵的振荡特性有调制作用,增大失谐量,场熵的最大值减小,振荡频率增大,由初始时刻的零值增大到最大值所需的时间也增大;光场的平均光子数太大或太小都不利于原子与光场之间的纠缠.     

运动纠缠双原子与二项式光场相互作用的纠缠特性

本文主要利用量子熵理论,讨论运动纠缠双原子与二项式光场的量子纠缠特性随时间的演化规律,结果表明:光场与原子纠缠度依赖于场模结构参数、光场的调节参量以及光子数.场模结构参数改变,影响纠缠周期性的变化且纠缠度随其增大而降低;当场调节参数处于中间值时,场熵呈明显周期性变化,系统纠缠度最大,退纠缠持续时间最短;光子数的改变不影响场熵演化的周期性,但是会影响周期内振荡频率和纠缠度的最大值.     

Horizon Entropy

Although the laws of thermodynamics are well established for black hole horizons, much less has been said in the literature to support the extension of these laws to more general settings such as an asymptotic de Sitter horizon or a Rindler horizon (the event horizon of an asymptotic uniformly accelerated observer). In the present paper we review the results that have been previously established and argue that the laws of black hole thermodynamics, as well as their underlying statistical mechanical content, extend quite generally to what we call here causal horizons. The root of this generalization is the local notion of horizon entropy density.     

Algebraic Entropy

For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the irreversibility of the map. We indicate how it can be exactly calculated. Received: 20 May 1998 / Accepted: 2 February 1999     

Entropy inequalities

Some inequalities and relations among entropies of reduced quantum mechanical density matrices are discussed and proved. While these are not as strong as those available for classical systems they are nonetheless powerful enough to establish the existence of the limiting mean entropy for translationally invariant states of quantum continuous systems.Work supported by National Science Foundation Grant GP-9414.     

Whose Entropy: A Maximal Entropy Analysis of Phosphorylation Signaling

High throughput experiments, characteristic of studies in systems biology, produce large output data sets often at different time points or under a variety of related conditions or for different patients. In several recent papers the data is modeled by using a distribution of maximal information-theoretic entropy. We pose the question: ‘whose entropy’ meaning how do we select the variables whose distribution should be compared to that of maximal entropy. The point is that different choices can lead to different answers. Due to the technological advances that allow for the system-wide measurement of hundreds to thousands of events from biological samples, addressing this question is now part of the analysis of systems biology datasets. The analysis of the extent of phosphorylation in reference to the transformation potency of Bcr-Abl fusion oncogene mutants is used as a biological example. The approach taken seeks to use entropy not simply as a statistical measure of dispersion but as a physical, thermodynamic, state function. This highlights the dilemma of what are the variables that describe the state of the signaling network. Is what matters Boolean, spin-like, variables that specify whether a particular phosphorylation site is or is not actually phosphorylated. Or does the actual extent of phosphorylation matter. Last but not least is the possibility that in a signaling network some few specific phosphorylation sites are the key to the signal transduction even though these sites are not at any time abundantly phosphorylated in an absolute sense.     

Relative Entropy and Relative Entropy of Entanglement for Infinite-Dimensional Systems

In this paper, firstly, we derive some inequalities about the relative entropy for infinite-dimensional quantum systems. Secondly, we propose a new measurement based on the relative entropy of entanglement for infinite-dimensional systems with bounded mean energy, and give a lower bound on this entanglement measure. Lastly, we generalize this measure to multi-partite quantum systems.     

Entropy and gravitation

Einstein's gravitational theory is analyzed from a thermodynamic point of view. A thermodynamic potential characterizing the sources of gravitational fields is presented. By means of this potential the entropy production density is derived. Einstein's equations with dissipative terms appear as linear phenomenological laws in the sense of irreversible thermodynamics. Some thermodynamic influences on gravitational phenomena are discussed.     

Zero Entropy Systems

This paper introduces the notion of entropy dimension to measure the complexity of zero entropy dynamical systems, including the probabilistic and the topological versions. These notions are isomorphism invariants for measure-preserving transformation and continuity. We discuss basic propositions for entropy dimension and construct some examples to show that the topological entropy dimension attains any value between 0 and 1. This paper also gives a symbolic subspace to achieve zero topological entropy, but with full entropy dimension.     

Entropy and anisotropy

We address the problem of defining the concept of entropy for anisotropic cosmological models. In particular, we analyze for the Bianchi I and V models the entropy which follows from postulating the validity of the laws of standard thermodynamics in cosmology. Moreover, we analyze the Cardy–Verlinde construction of entropy and show that it cannot be associated with the one following from relativistic thermodynamics.