On the Relationship Between Entropy and Enthalpy of Grain Boundary Segregation

An extensive study of anisotropy of grain boundary segregation in -iron, performed in the last decade, confirmed the existence of a linear relationship between entropy and enthalpy of solute segregation at individual grain boundaries. A thermodynamic analysis of this relationship is performed in the present work. It is shown that this dependence defines a compensation temperature and an entropy-like parameter. The compensation temperature is not necessarily connected with a phase transformation, but it represents exclusively a mean temperature at which all boundaries approach to a mean value of the Gibbs free energy of segregation. The most important consequences of this dependence are outlined: a reversed anisotropy of grain boundary segregation at temperatures above the compensation temperature, and a new method for the prediction of the enthalpy and entropy of solute segregation at individual grain boundaries.     

缓变动态Kerr-Newman黑洞的量子热力学性质

引入局域热平衡概念，用Damour-Ruffini方法和薄膜模型研究了缓变动态Kerr-Newman黑洞的Hawking辐射和熵.得到了黑洞的Hawking温度和辐射谱公式，Hawking温度随时间和视界面上的位置而变化，辐射谱为准黑体谱；计算了黑洞熵，当取与静态球对称黑洞情况相同的截断关系时便得到了黑洞的Bekenstein-Hawking熵.结果表明，缓变动态黑洞的温度是局域量，缓变动态黑洞的熵与稳态黑洞情况一样正比于黑洞视界面面积. 关键词： 缓变动态黑洞 Hawking辐射 黑洞熵     

Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. 145:1275, 2011). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.     

Local entropy and structure in a two-dimensional frustrated system

We calculate the local contributions to the Shannon entropy and excess entropy and use these information theoretic measures as quantitative probes of the order arising from quenched disorder in the diluted Ising antiferromagnet on a triangular lattice. When one sublattice is sufficiently diluted, the system undergoes a temperature-driven phase transition, with the other two sublattices developing magnetizations of equal magnitude and opposite sign as the system is cooled.(1) The diluted sublattice has no net magnetization but exhibits spin glass ordering. The distribution of local entropies shows a dramatic broadening at low temperatures; this indicates that the system's total entropy is not shared equally across the lattice. The entropy contributions from some regions exhibit local reentrance, although the entropy of the system decreases monotonically as expected. The average excess entropy shows a sharp peak at the critical temperature, showing that the excess entropy is sensitive to the structural changes that occur as a result of the spin glass ordering.     

Universal Scaling Law for Atomic Diffusion and Viscosity in Liquid Metals

The recently proposed scaling law relating the diffusion coefficient and the excess entropy of liquid [Samanta A et al. 2004 Phys. Reu. Lett. 92 145901; Dzugutov M 1996 Nature 381 137], and a quasi-universal relationship between the transport coefficients and excess entropy of dense fluids [Rosenfeld Y 1977 Phys. Rev. A 15 2545],are tested for diverse liquid metals using molecular dynamics simulations. Interatomic potentials derived from the glue potential and second-moment approximation of tight-binding scheme are used to study liquid metals.Our simulation results give sound support to the above-mentioned universal scaling laws. Following Dzugutov,we have also reached a new universal scaling relationship between the viscosity coefficient and excess entropy.The simulation results suggest that the reduced transport coefficients can be expressed approximately in terms of the corresponding packing density.     

Thermodynamic stability of binary nanocrystalline alloys: analysis of solute and excess vacancy

Regarding that the excess volume in grain boundaries (GBs) is released as the vacancies which are accommodated by the crystal bulk during grain growth, a free-energy function for binary nanocrystalline solid solution is proposed, based on the pairwise nearest-neighbor interactions. The model, for the given composition and temperature, predicts an equilibrium grain size, subjected to a mixed effect due to solute segregation and due to excess vacancies. Furthermore, excess-vacancy-inhibited grain coarsening can be attained, which plays a minor role in holding the thermal stability of nanocrystalline alloys, as compared to the effect of solute segregation.     

Solid solutions of hydrogen in gold,silver and copper

The temperature variation of the hydrogen solubility of copper, silver, and gold in equilibrium with H₂-gas at atmospheric pressure has been measured. Values for the relative partial enthalpy and partial excess entropy of the interstitially dissolved hydrogen atoms have been estimated from the solubility data.The experimental data are compared with those of previous investigations. The partial entropy values obtained for, copper and silver show a ‘regular’ behavior when compared with partial entropies for other cubic metals having a small occludive capacity for hydrogen. The gold-hydrogen system is, however, anomalous and has a partial excess entropy which is essentially zero.     

Glass Transition Temperature of Water： from Simulations of Diffusion and Excess Entropy

We report a computer simulation study of the glass transition of water with SP2 potential. The temperature dependences of the diffusion coefficient and the excess entropy on cooling process are calculated. It is found that both the diffusion coefficient and the excess entropy show a break point at 160K. Our results support the viewpoint that the glass transition temperature is 160K. According to the calculated viscosity, we obtain a fragility index of water to be 326, which is much larger than the value accepted before.     

Quantum Thermal Effect of Nonstationary Kerr-Newman Black Hole

The Hawking radiation and the entropy of non-stationary Kerr-Newman black hole whose metric changes slowly are calculated via the method of Damour etc. and the thin film brick-wall model. First, we obtain the Hawking radiation temperature and the thermal spectrum formula. Second, we get the entropy density at every point of the horizon surface as well as the total entropy of the black hole, which is just the Bekenstein-Hawking entropy and relies on the notion of the local equilibrium crucially that can be met if the evaporation and the accretion of the black hole is negligible. The results show that the temperature of the event horizon depends on the time and the angle, and the entropy of the non-stationary black hole is also proportional to the horizon area with appropriate cutoff relationship as in the case of stationary black holes.     

Permutation complexity via duality between values and orderings

We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of all permutations of the same length. Second, on this basis, we give an elementary alternative proof of the equality between the permutation entropy rate and the entropy rate for a finite-state stationary stochastic processes first proved in [J.M. Amigó, M.B. Kennel, L. Kocarev, The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems, Physica D 210 (2005) 77-95]. Third, we show that further information on the relationship between the structure of values and the structure of orderings for finite-state stationary stochastic processes beyond the entropy rate can be obtained from the established duality. In particular, we prove that the permutation excess entropy is equal to the excess entropy, which is a measure of global correlation present in a stationary stochastic process, for finite-state stationary ergodic Markov processes.     

Maslov distribution and formulas for the entropy

The Maslov distribution for a system of identical particles is used. The entropy and some other thermodynamical characteristics of this system are found for diverse fractal dimensions. A general formula for the entropy is established, which shows that the entropy is proportional to the derivative of the system energy with respect to the temperature. It is shown that a parastatistical parameter b, which is introduced formally, is related to the temperature of the system indeed. The nature of the phase transition in the system is studied in the two-dimensional case.     

Estimating the entropy of liquids from atom–atom radial distribution functions: silica,beryllium fluoride and water

Molecular dynamics simulations of water, liquid beryllium fluoride and silica melt are used to study the accuracy with which the entropy of ionic and molecular liquids can be estimated from atom–atom radial distribution function data. The pair correlation entropy is demonstrated to be sufficiently accurate that the density–temperature regime of anomalous behaviour as well as the strength of the entropy anomaly can be predicted reliably for both ionic melts as well as different rigid-body pair potentials for water. Errors in the total thermodynamic entropy for ionic melts due to the pair correlation approximation are of the order of 10% or less for most state points, but can be significantly larger in the anomalous regime at very low temperatures. In the case of water, the rigid-body constraints result in larger errors in the pair correlation approximation, between 20 and 30%, for most state points. Comparison of the excess entropy, S _e, of ionic melts with the pair correlation entropy, S ₂, shows that the temperature dependence of S _e is well described by T ^?2/5 scaling across both the normal and anomalous regimes, unlike in the case of S ₂. The residual multiparticle entropy, ΔS = S _e ? S ₂, shows a strong negative correlation with tetrahedral order in the anomalous regime.     

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

The maximum entropy principle consists of two steps: The first step is to find the distribution which maximizes entropy under given constraints. The second step is to calculate the corresponding thermodynamic quantities. The second part is determined by Lagrange multipliers’ relation to the measurable physical quantities as temperature or Helmholtz free energy/free entropy. We show that for a given MaxEnt distribution, the whole class of entropies and constraints leads to the same distribution but generally different thermodynamics. Two simple classes of transformations that preserve the MaxEnt distributions are studied: The first case is a transform of the entropy to an arbitrary increasing function of that entropy. The second case is the transform of the energetic constraint to a combination of the normalization and energetic constraints. We derive group transformations of the Lagrange multipliers corresponding to these transformations and determine their connections to thermodynamic quantities. For each case, we provide a simple example of this transformation.     

Can experiments select the configurational component of excess entropy?

Configurational entropy is frequently used to rationalize the structural dynamics of glass-forming liquids. The main problem with this concept is that it is not directly accessible to experiments. We introduce a procedure to estimate the configurational component of the excess entropy of a liquid --specifically, the configurational-entropy contribution from the structural relaxation process-- through a combined investigation of dynamic and thermodynamic properties as functions of temperature and pressure. We test our method on orthoterphenyl, salol, and glycerol, and find that the fraction of excess entropy that arises from structural configurations is about 70% for all three materials.Received: 29 April 2004, Published online: 29 June 2004PACS: 64.70.Pf Glass transitions - 78.35. + c Brillouin and Rayleigh scattering; other light scattering - 77.22.Gm Dielectric loss and relaxation     

A model of the kinetics and equilibria of surface segregation in the monolayer regime

A kinetic model of surface segregation based on foreign atom movement in an appropriate potential is developed. It is used to calculate the time and temperature dependence of surface concentration and the concentration distribution perpendicular to the surface for the case of structure limited surface enrichment. The results give an explanation for Auger electron spectroscopy obervations of the segregation of tin at the surface of copper single crystals. In-depth profiles of composition obtained by sputtering are in agreement with predictions from the model. Deviations from other models of segregation kinetics are briefly discussed.     

A measure of statistical complexity based on predictive information with application to finite spin systems

We propose the binding information as an information theoretic measure of complexity between multiple random variables, such as those found in the Ising or Potts models of interacting spins, and compare it with several previously proposed measures of statistical complexity, including excess entropy, Bialek et al.?s predictive information, and the multi-information. We discuss and prove some of the properties of binding information, particularly in relation to multi-information and entropy, and show that, in the case of binary random variables, the processes which maximise binding information are the ‘parity’ processes. The computation of binding information is demonstrated on Ising models of finite spin systems, showing that various upper and lower bounds are respected and also that there is a strong relationship between the introduction of high-order interactions and an increase of binding-information. Finally we discuss some of the implications this has for the use of the binding information as a measure of complexity.     

Ag-Cu双金属团簇中Ag原子偏析行为的 分子动力学研究

采用了恒温分子动力学方法系统模拟研究了不同尺寸不同组分的Ag-Cu双金属团簇的退火过程。分析低温退火结构可得团簇中Ag原子的偏析行为：在Ag原子所占比率较少时,Ag原子全部占据在团簇表面;随着Ag原子数的增多,直到Ag和Cu的比率接近时,绝大多数Ag原子仍占据在团簇表面;这与实验观测Ag-Cu混合团簇中Ag原子的偏析行为完全一致。通过细致研究Ag-Cu双金属团簇中Ag原子的偏析行为与团簇尺寸、组分和温度的关系发现：当Ag原子所占比重明显少于Cu原子时,在各不同尺寸下,Ag原子偏析温度点均高于熔点,即在熔点以上一定温度范围内仍会出现Ag原子的偏析现象;当Ag原子所占比重明显多于Cu原子时,在各不同尺寸下,体系偏析温度点均低于团簇熔点;对于较大尺寸团簇,在Ag原子所占比重接近于Cu原子时,体系偏析温度点与团簇熔点相同。     

Surfactant-induced surface freezing at the alkane-water interface

Long-chain alkanes exhibit surface freezing at the alkane-air but not the alkane-water interface. Ellipsometry and surface tensiometry are used to show that a simple cationic surfactant, hexadecyltrimethylammonium bromide (CTAB), can induce surface freezing at the tetradecane-water interface even when present in mole fractions as low as 0.1. The surface-freezing temperature T(s) is a linear function of the interfacial excess of CTAB. The excess surface entropy below T(s), S(sigma)=-0.76+/-0.02 mJ K-1 m(-2), is consistent with a rotator phase. Ellipsometry provides strong evidence for a frozen monolayer in which the chains are oriented near the surface normal.     

Permutation approach to finite-alphabet stationary stochastic processes based on the duality between values and orderings

The duality between values and orderings is a powerful tool to discuss relationships between various information-theoretic measures and their permutation analogues for discrete-time finite-alphabet stationary stochastic processes (SSPs). Applying it to output processes of hidden Markov models with ergodic internal processes, we have shown in our previous work that the excess entropy and the transfer entropy rate coincide with their permutation analogues. In this paper, we discuss two permutation characterizations of the two measures for general ergodic SSPs not necessarily having the Markov property assumed in our previous work. In the first approach, we show that the excess entropy and the transfer entropy rate of an ergodic SSP can be obtained as the limits of permutation analogues of them for the N-th order approximation by hidden Markov models, respectively. In the second approach, we employ the modified permutation partition of the set of words which considers equalities of symbols in addition to permutations of words. We show that the excess entropy and the transfer entropy rate of an ergodic SSP are equal to their modified permutation analogues, respectively.