熵的一种通俗教法

熵如力、能量和动量一样是物理学中一个重要概念,若能用一种通俗易懂的方法设计熵的教学,对文科物理的教学有重要意义.为此本文提出了一种通俗的熵的教法,这一教法不需要学生学习热力学第二定律也可以建立熵的概念.具体教学设计如下:通过日常生活例子引入熵的概念(也就是玻尔兹曼熵),设计两个例子让学生会计算熵,通过具体问题的讨论让学生充分理解熵的意义,通过一个实例由玻尔兹曼熵引入克劳修斯熵公式,设计一个演示实验强化教学效果,将熵与环境保护联系起来融入人文情怀,最后还强调了熵计算的不同层次.教学设计完全采用基于问题学习(PBL)的教学模式.     

熵和信息及其在生命系统中的应用

介绍了克劳修斯熵、玻耳兹曼熵和信息熵,讨论了这三种熵之间的关系。并把熵与信息的关系应用到生命系统中得到一个典型的大肠杆菌细胞的信息量约为4.6×1 010比特。     

简论热力学熵、信息熵及熵的泛化

 热力学熵 熵是克劳修斯于1865年定义并命名的一个热力学系统的状态函数,它严格应用于系统的热运动,故又称“热力学熵”。     

漫谈熵

熵是物理中的一个既重要又微妙的概念。文章从物理学引入熵谈起,依次讨论熵与热力学第二定律、熵的统计力学定义、熵增与基础物理理论的矛盾,以及时间箭头与玻尔兹曼大脑,最后介绍著名的黑洞熵。     

计算机能耗理论下限推导的教学探讨

新概念物理教程热学中将玻尔兹曼熵和信息熵相比得到计算机处理信息能耗的理论下限,受限于篇幅的原因,作者讲解较为简略,给学习者对知识的理解增加了难度.本文就课本中的处理方法提出几点疑问,进一步给出计算机处理信息能耗理论下限的一般解释.在此基础上就当前一些学者认为玻尔兹曼熵与信息熵等价的观点作出辨析.     

关于克劳修斯方法对可逆和不可逆过程(循环)的处理

介绍了克劳修斯方法对可逆和不可逆过程(循环)的处理,提出了处理不可逆过程的方法,论证了处理方法与克劳修斯方程的一致性,论述了克劳修斯方法的实质和意义;简单介绍了熵的另一个导出方法,比较了两种方法对绝热过程的处理,指出克劳修斯方法存在一个假设条件.     

运动原子与光场依赖强度纠缠下最佳熵压缩态的制备和控制

运用量子信息熵理论,研究了运动二能级原子与光场依赖强度纠缠下最佳熵压缩态的制备和控制;比较了分别从基于信息熵不确定关系和海森堡不确定关系出发得出的结果;分析了制备原子最佳熵压缩态的充要条件,并进行了数值验证.考察了场模结构参数对最佳熵压缩态的影响.结果表明,信息熵压缩是对原子压缩效应的高灵敏量度;控制原子与场的相互作用时间,斩断原子和场的纠缠,选择原子的相干性,调节系统的相对位相可制备原子最佳熵压缩态;控制场模结构参数,可获得持续的原子最佳熵压缩态. 关键词： 依赖强度耦合 场模结构参数 最佳熵压缩态     

非高斯噪声驱动的双奇异随机系统的熵流与熵产生

研究了一类受非高斯噪声驱动的双奇异随机系统,应用路径积分法和变换的方法得到了该系统对应的Fokker-Plank方程,并结合Shannon信息熵的定义给出了此类系统的熵流与熵产生随时间演化的表达式,分析了非平衡约束下所引入的系统耗散参数、奇异性强度参数、噪声相关时间和噪声偏离参数对熵流与熵产生的影响. 关键词： 信息熵 熵流与熵产生 非高斯噪声 双奇异随机系统     

与量子光场相互作用的运动原子的熵压缩

运用量子信息熵理论,研究了与量子光场相互作用的二能级运动原子的熵压缩,讨论了原子运动和场模结构对原子熵压缩的影响,并且比较了分别从基于信息熵测不准关系和海森伯测不准关系出发得出的结果,表明原子的运动导致了原子熵压缩的周期性演化;随着场模结构参量的增大,熵压缩的演化周期缩短,压缩时间延长;选择适当的系统参量,运动原子能够呈现长时间的持续熵压缩效应。当原子反转为零时,基于海伯堡测不准关系的方差压缩定义不再有效,而熵压缩实现了对原子压缩效应的高灵敏量度。     

色噪声驱动的双奇异随机系统的熵流与熵产生

讨论一类 (非平衡约束下) 高斯色噪声驱动的双奇异随机系统对应的Fokker-Planck方程，结合Shannon信息熵定义给出此类系统的熵流、熵产生随时间演化的精确表达式.分析(非平衡约束下)所引入的奇异性强度参数、噪声相关时间与耗散参数的相互作用以及对熵流、熵产生的显著影响. 关键词： 信息熵 熵流与熵产生 双奇异随机系统 高斯色噪声     

A method to calculate Boltzmann entropy

A method is proposed to calculate the Boltzmann non equilibrium entropy as a Taylor series expansion in terms of the successive moments of the velocity distribution function. As a first application, the entropy of the BKW solution of the Boltzmann equation is calculated for both even and odd dimensions. The properties of the entropy of the Tjon Wu modeld=2) are studied and a quantitative condition is derived, showing that the McKean conjecture is incorrect. As a second application of the method, the entropy of one of the solutions of the very hard particle model for the Boltzmann equation is also derived.     

Topological permutation entropy

Permutation entropy quantifies the diversity of possible ordering of the successively observed values a random or deterministic system can take, just as Shannon entropy quantifies the diversity of the values themselves. When the observable or state variable has a natural order relation, making permutation entropy possible to compute, then the asymptotic rate of growth in permutation entropy with word length forms an alternative means of describing the intrinsic entropy rate of a source. Herein, extending a previous result on metric entropy rate, we show that the topological permutation entropy rate for expansive maps equals the conventional topological entropy rate familiar from symbolic dynamics. This result is not limited to one-dimensional maps.     

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic "Landau" potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.     

Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation

We first consider the Boltzmann equation with a collision kernel such that all kinematically possible collisions are run at equal rates. This is the simplest Boltzmann equation having the compressible Euler equations as a scaling limit. For it we prove a stability result for theH-theorem which says that when the entropy production is small, the solution of the spatially homogeneous Boltzmann equation is necessarily close to equilibrium in the entropie sense, and therefore strongL ¹ sense. We use this to prove that solutions to the spatially homogeneous Boltzmann equation converge to equilibrium in the entropie sense with a rate of convergence which is uniform in the initial condition for all initial conditions belonging to certain natural regularity classes. Every initial condition with finite entropy andp ^th velocity moment for some p>2 belongs to such a class. We then extend these results by a simple monotonicity argument to the case where the collision rate is uniformly bounded below, which covers a wide class of slightly modified physical collision kernels. These results are the basis of a study of the relation between scaling limits of solutions of the Boltzmann equation and hydrodynamics which will be developed in subsequent papers; the program is described here.On leave from School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332.On leave from C.F.M.C. and Departamento de Matemática da Faculdade de Ciencias de Lisboa, 1700 Lisboa codex, Portugal.     

Information entropy for static spherically symmetric black holes

By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein--Hawking entropy when the suitable cutoff factor is adopted.     

双光子过程中任意初态原子的信息熵压缩

运用量子信息熵理论研究了双光子过程中任意初态二能级原子与相干场相互作用的信息熵压缩，讨论了系统初态对原子信息熵压缩的影响. 并且比较了分别从基于信息熵不确定关系和海森伯不确定关系出发得出的结果. 结果表明通过选择适当初始的原子分布角，原子的混合度和相干场的位相角，可以分别控制原子信息熵压缩的偶极矩分量数、压缩频率、压缩幅度和压缩方向. 当原子反转为零时，基于海森堡不确定关系的方差压缩定义不再有效，而信息熵压缩实现了对原子压缩效应的高灵敏量度. 关键词： 二能级原子 双光子过程 信息熵压缩 方差压缩     

Temperature, entropy, and kinetic theory

The relation between the concepts of temperature and entropy and the kinetic theory of gases is discussed, with particular attention to the aspects which are frequently treated as obvious or not even mentioned. In order to show that the usual thermodynamic relations are by no means obvious and may be contradictory, the model of a discrete velocity gas is used. It is also shown that the usual relation between the entropy rate and the heat supplied to a gas is not valid (even close to equilibrium) unless the theory is Galilei invariant (which is obviously not the case for a discrete velocity gas) and must be replaced by another one that eliminates all the paradoxical aspects of the matter.     

双模纠缠相干光场控制下双光子过程中有效二能级原子的信息熵压缩

根据量子信息理论,研究了与双模纠缠相干场相互作用双光子过程中有效二能级原子的信息熵压缩.讨论了场的初态对信息熵压缩的因影响,并且比较了分别从基于信息熵测不准关系和海森堡测不准关系出发得出的结果.结果表明:信息熵压缩的稳定周期性、压缩方向分别由场的平均光子数和方向角控制,场的纠缠度对信息熵压缩不产生影响.信息熵压缩实现了对原子压缩效应的高灵敏量度.