On information,negentropy andH-theorem

The paper deals with the imprtance of the Kullback descrimination information in the statistical characterization of negentropy of non-equilibrium state and the irreversibility of a classical dynamical system. The theory based on the Kullback discrimination information as theH-function gives new insight into the interrelation between the concepts of coarse-graining and the principle of sufficiency leading to important statistical characterization of thermal equilibrium of a closed system.     

Negative entropy of mixing for vanadium-platinum solutions

The phonon densities of states for pure vanadium and the solid solutions V-6.25% Ni, Pd, Pt were determined from inelastic neutron scattering measurements. The solute atoms caused a large stiffening of the phonons, resulting in large, negative vibrational entropies of mixing. For V-6.25%Pt, the negative vibrational entropy of mixing exceeds the conventional positive chemical entropy of mixing. This negative total entropy of mixing should extend to lower concentrations of Pt, and the effect on the bcc solvus line is discussed. The experimental data were inverted to obtain interatomic force constants by using a Born-von Kármán model with an iterative optimization algorithm. The stiffening of bonds responsible for the decrease of entropy was found to occur mainly in first-nearest-neighbor solute-host bonds, and correlates in part with the solute metallic radius.     

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。     

On entropy production

We investigate the case of a dynamical system when irreversible time evolution is generated by a nonHermitian superoperator on the states of the system. We introduce a generalized scalar product which can be used to construct a monotonically changing functional of the state, a generalized entropy. This will depend on the level of system dynamics described by the evolution equation. In this paper we consider the special case when the irreversibility derives from imbedding the system of interest into a thermal reservoir. The ensuing time evolution is shown to be compatible both with equilibrium thermodynamics and the entropy production near the final steady state. In particular, Prigogine’s principle of minimum entropy production is discussed. Also the limit of zero temperature is considered. We present comments on earlier treatments.     

On entropy, financial markets and minority games

The paper builds upon an earlier statistical analysis of financial time series with Shannon information entropy, published in [L. Molgedey, W. Ebeling, Local order, entropy and predictability of financial time series, European Physical Journal B—Condensed Matter and Complex Systems 15/4 (2000) 733-737]. A novel generic procedure is proposed for making multistep-ahead predictions of time series by building a statistical model of entropy. The approach is first demonstrated on the chaotic Mackey-Glass time series and later applied to Japanese Yen/US dollar intraday currency data. The paper also reinterprets Minority Games [E. Moro, The minority game: An introductory guide, Advances in Condensed Matter and Statistical Physics (2004)] within the context of physical entropy, and uses models derived from minority game theory as a tool for measuring the entropy of a model in response to time series. This entropy conditional upon a model is subsequently used in place of information-theoretic entropy in the proposed multistep prediction algorithm.     

快速发展中的高熵溶体合金

多主元高熵合金是依据等原子比、高混合熵这样的合金设计理念而发展起来的,与传统的单主元合金或两主元金属间化合物不同,它一般由5种以上主要元素构成,各种组元协同起作用,这使得其组织和性能特点在许多方面有别于传统合金.现有的研究表明,作为一个材料研究的新兴领域,高熵合金有着很高的研究价值与应用前景.文章介绍了高熵合金的定义、组织、性能特点及其应用,并介绍了该方向的一些最新研究进展.     

快速发展中的高熵溶体合金

多主元高熵合金是依据等原子比、高混合熵这样的合金设计理念而发展起来的,与传统的单主元合金或两主元金属间化合物不同,它一般由5种以上主要元素构成,各种组元协同起作用,这使得其组织和性能特点在许多方面有别于传统合金.现有的研究表明,作为一个材料研究的新兴领域,高熵合金有着很高的研究价值与应用前景.文章介绍了高熵合金的定义、组织、性能特点及其应用,并介绍了该方向的一些最新研究进展.     

On the relative entropy

ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent _A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent _A ^A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent ^S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent ^S : monotonicity, concavity,w* upper semicontinuity, etc.     

A new expression for the combinatorial entropy of mixing in liquid mixtures

In the classic expression for the combinatorial entropy in terms of the mole fractions x_A and x_B′ the space unoccupied by the B molecules appears for them as divided in numerable parts, each belonging to an A molecule. In the Flory-Huggins expression based on the volume fractions φ_A and φ_B the space unoccupied by the B molecules is for them a continuum, not parcelled out in portions based on A standards. However in a solution containing n_B moles of B for a total number of moles n, the border of a B molecule is separated from that of the nearest B on the average by a distance equal to ((n/n_B)^1/2?1) times the mean diameter of the A molecules. Thus, there exists still in the liquid, directions for the B molecules which can be divided according to A standards. Based on this consideration, a new expression is derived for the combinatorial entropy of liquid mixtures which contains a “numerable” part besides a “continuous” part. on applying this equation for the prediction of the solubility of solid n-alkanes in liquid alkanes and neglecting non-ideality effects, the predicted values agree much better with the experimental ones than those deduced from the classic or from the Flory-Huggins expression.     

On the entropy of fusion

The asymptotic value of the melting entropy, i.e. ΔS_f = R ln 2 for vanishing relative change of volume on melting, can be derived from the vibrational entropy due to vibrating dislocations, which are introduced into a material on melting.     

On the entropy of melting

The necessity of general interpretation of the phenomenon of melting, including subtances with dp/dT < 0, is stressed. The latter substances do not satisfy the regularity that for ΔV/V_s = 0 the asymptotic value of ΔS/R amounts to ln2.     

On the entropy of melting

The analysis of experimental data shows that the function δS/R = f(δV/V_S), where δS/R is the entropy of melting and δV/V_S the relative change of volume at melting, is the same for argon and sodium. The melting entropy of these substances tends to Rln2, when δV/V_S vanishes.     

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。     

On the relation between correlation dimension,approximate entropy and sample entropy parameters,and a fast algorithm for their calculation

We explore the relation between correlation dimension, approximate entropy and sample entropy parameters, which are commonly used in nonlinear systems analysis. Using theoretical considerations we identify the points which are shared by all these complexity algorithms and show explicitly that the above parameters are intimately connected and mutually interdependent. A new geometrical interpretation of sample entropy and correlation dimension is provided and the consequences for the interpretation of sample entropy, its relative consistency and some of the algorithms for parameter selection for this quantity are discussed. To get an exact algorithmic relation between the three parameters we construct a very fast algorithm for simultaneous calculations of the above, which uses the full time series as the source of templates, rather than the usual 10%. This algorithm can be used in medical applications of complexity theory, as it can calculate all three parameters for a realistic recording of 10⁴${10}^4$ points within minutes with the use of an average notebook computer.     

On generalized entropy measures and pathways

Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the recursivity postulate automatically determines the logarithmic functional form for Shannon entropy. Due to the logarithmic nature, Shannon entropy naturally gives rise to additivity, when applied to situations having product probability property. It is argued that the natural process is non-additivity, important, for example, in statistical mechanics [C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1988) 479-487; E.G.D. Cohen, Boltzmann and Einstein: statistics and dynamics—an unsolved problem, Pramana 64 (2005) 635-643.], even in product probability property situations and additivity can hold due to the involvement of a recursivity postulate leading to a logarithmic function. Generalized entropies are introduced and some of their properties are examined. Situations are examined where a generalized entropy of order α leads to pathway models, exponential and power law behavior and related differential equations. Connection of this entropy to Kerridge's measure of “inaccuracy” is also explored.     

On the entropy of nonequilibrium states

A definition originally proposed by H. S. Green is used to calculate the entropy of nonequilibrium steady states. This definition provides a well-defined coarse graining of the entropy. Although the dimension of the phase space accessible to nonequilibrium steady states is less than the ostensible dimension of that space, the Green entropy is computed from within the accessible phase space, thereby avoiding the divergences inherent in the fine-grained entropy. It is shown that the Green entropy is a maximum at equilibrium and that away from equilibrium, the thermodynamic temperature computed from the Green entropy is different from the kinetic temperature.