Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

Excess molar enthalpies of binary mixtures of 1-hexene with some cyclic and aromatic hydrocarbons at 298.15 K

Microcalorimetric measurements of excess molar enthalpies, at 298.15 K, are reported for the four binary systems formed by mixing 1-hexene with the cycloalkanes: cyclohexane and methylcyclohexane, and with the aromatic hydrocarcons: benzene and toluene. Smooth Redlich-Kister representations of the results are presented. It was found that the Liebermann-Fried model also provided good representations of the results.     

Excess enthalpies of some 2-alkanone + 1-chloroalkane binary mixtures at 25 and 35°C

Excess molar enthalpies h^E at 25 and 35° C and atmospheric pressure, are reported for the binary mixtures formed by a 2-butanone and 2-pentanone with 1-chlorobutane, 1-chloropentane, 1-chlorohexane, or 1-chlorooctane. The h^E values for all the mixtures are positive, increasing as the 1-chloroalkane length increases and as the ketone length decreases. Excess molar enthalpies depend slightly on the temperature. The experimental values together with those from the literature were used to calculate the interaction parameters for the Dang-Tassios version of the UNIFAC model.Communicated at the Festsymposium celebrating Dr. Henry V. Kehiaian's 60^th birthday, Clermont-Ferrand, France, 17–18 May 1990.     

Spectral distributions in nuclei: General principles and applications

The subject of spectral distribution methods where one derives and applies the locally smoothed forms of observables in nuclei is briefly reviewed. It is well understood that the local forms (with respect to energy) of the level density function, expectation values and strength densities are Gaussian, linear (or ratio of Gaussians) and a bivariate Gaussian respectively. To accomodate symmetries in the above forms, one has to deal with multivariate distributions in general; for example the angular-momentum (J) decomposition leads to a bivariate Gaussian form for the level density. These results extend to indefinitely large spaces by method of partitioning and they generate convolution forms. The origin of these remarkable spectral properties is discussed and shell model examples are given to substantiate their applicability to nuclear systems. Spectral distribution theory is a practical, usable theory because the smoothed forms are defined in terms of traces of low particle-rank operators, and the trace information propagates. Finally we discuss the application of the spectral methods for a wide range of nuclear problems; these include binding energies, orbit occupancies, electromagnetic andβ-decay sum rule quantities, analysis of operators, symmetry breaking, numerical level densities, and determination of bounds on time-reversal non-invariant part of nucleon-nucleon interaction.     

正已醇-邻、间、对二甲苯二元系固液相平衡

Melting temperatures have been measured and the solid-liquid phase diagrams constructed for 1-hexanol＋o-xylene, 1-hexanol＋m-xylene and 1-hexanol＋p-xylene. They are simple eutectic systems. Excess mole Gibbs free energies were calculated at 298.15K, showing larger positive deviations from ideal-solution behavior. The largest values of GmE are 711、 650 and 800 J•mol-1 for {o-C6H4(CH3)2＋C6H13OH}、 {m-C6H4(CH3)2 ＋ C6H13OH} and {p-C6H4(CH3)2＋C6H13OH} respectively.     

Topological investigations of molar excess volumes of quinoline with alkanols

Excess volumes V ^E of binary liquid mixtures of quinoline with alkanols have been determined from densities at 30°C as a function of composition. The excess volumes are negative over the whole mole fraction range for all the mixtures and decrease with increasing length of alkanol (C₁–C₁₀). The V^E data have been analyzed in terms of an approach which uses graph theoretical connectivity parameters of the third degrees for two components. The analysis gives information regarding associated species in the pure state and in the mixture. It is suggested that, in the mixture state, no change occurs in the association of alkanols.     

Hydrogen substitution effect on the solubility of perhalogenated compounds in ionic liquid [bmim][PF6]

Solubility behaviors of binary mixtures of CFCl₃ (R-11), CFCl₂-CF₂Cl (R-113), CHCl₃ (R-20), CDCl₃ (R-20-d), CHCl₂–CF₃ (R-123) with room-temperature ionic liquid [bmim][PF₆] (1-butyl-3-methylimidazolium hexafluorophosphate) have been investigated using the volumetric and cloud-point methods, since all the systems show liquid–liquid equilibria (LLE). Large immiscibility (LLE) gaps of the perhalogenated compounds (R-11 and R-113) in the ionic liquid have been drastically reduced by the addition of only one hydrogen (or deuterium) in these compounds. The R-123 + [bmim][PF₆] binary system belongs to the Type-V fluid behavior. Noticeably large negative values (−2 to −8 cm³ mol⁻¹) of the excess molar volume in the ionic liquid-rich side solution have been observed for all the present systems. Experimental LLE data have been well correlated by the use of the NRTL (non-random two liquid) activity coefficient model.     

S-Shaped composition dependence of excess thermodynamic quantities for cyclohexane mixtures with globular alkanes

Expansion coefficients , isothermal compressibilities, thermal pressure coefficients and heat capacities have been measured at 25°C for the cyclohexane+trans-decalin system. An S-shaped composition dependence, positivelnegative for highllow cyclohexane compositions is found for C _p ^E dV ^E /dT and the thermal expansion contribution to C _p ^E namely VT. The thermal motion contribution to C _p ^E , namely C _v is close to zero. The positive excursion of these mixing quantities at high cyclohexane content is anomalous. Correspondingly, the mixing quantity-VT deviates strongly in this region from the predicted equality with H ^E . The literature and this work show that all these excess quantities behave similarly for cyclohexane mixed with cyclooctane, methylcyclohexane and some highly branched alkanes. The unusual composition dependence of the thermodynamic quantities is consistent with order occurring when any large alkane molecule of globular shape is added to cyclohexane. This is speculatively associated with an interference by the globular alkane with the relatively free rotation of cyclohexane molecules.     

Physical and Chemical Properties of Dissolved Electrons (Excess Electrons)

Electrons produced in a gaseous, liquid, or solid solvent are called dissolved electrons or excess electrons. These excess electrons can exist as quasi-free particles of high mobility in a delocalized state, comparable with electrons in a metal; or as bound particles of low mobility they can be localized within narrow limits—in a solvent cavity formed by repulsive forces. Localized electrons can also be solvated like normal ions. Characteristically, such solvated electrons exhibit broad and extensive absorption spectra in the visible to near infrared spectral range. The localized and delocalized states of the excess electrons can be in equilibrium with each other, such that a continuous transition of the properties between the limiting extremes can be observed. The reactions of the excess electrons with suitable acceptors (substrates) are initiated by an attachment-detachment equilibrium A + e^? ? A^? which is followed by further chemical rearrangements. The rate constants of these reactions vary by more than 15 powers of ten depending on the substrates and the solvents. Most of the properties of excess electrons in solution can be interpreted by means of a model which is easily understandable but quantitatively evaluated only with considerable effort.