信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系--兼论玻尔兹曼熵和克劳修斯熵是否等价

论述了信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系;由不涉及具体系统的方法从玻尔兹曼关系、信息熵推导出了克劳修斯熵的表达式;指出玻尔兹曼熵与克劳修斯熵不是等价关系,而是玻尔兹曼熵包含克劳修斯熵,信息熵又包含玻尔兹曼熵。     

态函数熵的几种引入方法

熵在物理学中是一个十分重要的概念，但又是最为抽象的概念之一．本文从不同的角度出发给出熵的几种定义方法，并从多方面阐释熵的含义．     

Characteristics of the spatiotemporal distribution of daily extreme temperature events in China: Minimum temperature records in different climate states against the background of the most probable temperature

Based on the skewed function,the most probable temperature is defined and the spatiotemporal distributions of the frequencies and strengths of extreme temperature events in different climate states over China are investigated,where the climate states are referred to as State I,State II and State III,i.e.,the daily minimum temperature records of 1961-1990,1971-2000,and 1981-2009.The results show that in space the frequency of high temperature events in summer decreases clearly in the lower and middle reaches of the Yellow River in State I and that low temperature events decrease in northern China in State II.In the present state,the frequency of high temperature events increases significantly in most areas over China except the north east,while the frequency of low temperature events decreases mainly in north China and the regions between the Yangtze River and the Yellow River.The distributions of frequencies and strengths of extreme temperature events are consistent in space.The analysis of time evolution of extreme events shows that the occurrence of high temperature events become higher with the change in state,while that of low temperature events decreases.High temperature events are becoming stronger as well and deserve to be paid special attention.     

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.     

Schwarzschild-de Sitter黑洞宇宙视界量子态的熵

采用由广义不确定关系得到的新的态密度方程 ,研究了Schwarzchild deSitter时空背景下黑洞宇宙视界的熵 .利用新的态密度方程 ,克服了用brick wall模型方法计算黑洞熵 ,在消除紫外发散需取截断的不完善之处 ,以此揭示了黑洞熵与其视界面积成正比这一内在联系 ,进一步表明黑洞熵是视界面处量子态的熵     

Schwarzschild-de-Sitter黑洞宇宙视界量子态的熵

采用由广义不确定关系得到的新的态密度方程，研究了Schwarzchild-de-Sitter时空背景下黑洞宇宙视界的熵.利用新的态密度方程，克服了用brick wall模型方法计算黑洞熵，在消除紫外发散需取截断的不完善之处，以此揭示了黑洞熵与其视界面积成正比这一内在联系，进一步表明黑洞熵是视界面处量子态的熵. 关键词： 黑洞 广义不确定关系 态密度 熵     

Quantum uncertainty relations of Tsallis relative α entropy coherence based on MUBs

In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.     

Lattice Boltzmann simulation for the energy and entropy of excitable systems

The internal energy and the spatiotemporal entropy of excitable systems are investigated with the lattice Boltzmann method.The numerical results show that the breakup of spiral wave is attributed to the inadequate supply of energy,i.e.,the internal energy of system is smaller than the energy of self-sustained spiral wave.It is observed that the average internal energy of a regular wave state reduces with its spatiotemporal entropy decreasing.Interestingly,although the energy difference between two regular wave states is very small,the different states can be distinguished obviously due to the large difference between their spatiotemporal entropies.In addition,when the unstable spiral wave converts into the spatiotemporal chaos,the internal energy of system decreases,while the spatiotemporal entropy increases,which behaves as the thermodynamic entropy in an isolated system.     

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.     

A Boltzmann Equation Approach to the Dynamics of the Simple Piston

The evolution of a simple piston under a constant external force is investigated from a microscopic approach. Using Boltzmann's equation and simplifying assumptions it is shown that the system evolves towards equilibrium according to the macroscopic laws of thermodynamics: entropy production is positive and Onsager's relations are verified near equilibrium. Numerical simulations are presented which show that the evolution takes place in two stages: first a deterministic approach to the equilibrium position and then a stochastic motion around the equilibrium position. It also shows that the damping is not correctly described with these simplifying assumptions and a quantitative explanation of this effect remains an open problem.     

粒子数按高度的分布律中一个容易被忽视的问题

通过分析和计算表明重力场中粒子数按高度分布律里的ｎ０并非常数,它不仅与ｍ有关,而且还与Ｔ有关,从而指出并纠正了一些文献中存在的一个被忽视的问题。     

Theory of quantum fluctuations and the Onsager relations

A microscopic model is constructed within the theory of normal fluctuations for quantum systems, yielding an irreversible dynamics satisfying the Onsager relations. The property of return to equilibrium and the principle of minimal entropy production are proved.