A geometrical measure for entropy changes

The geometrical approach to statistical mechanics is used to discuss changes in entropy upon sequential displacements of the state of the system. An interpretation of the angle between two states in terms of entropy differences is thereby provided. A particular result of note is that any state can be resolved into a state of maximal entropy (both states having the same expectation values for the constraints) and an orthogonal component. A cosine law for the general case is also derived.     

Possibilistic networks for information retrieval

This paper proposes an information retrieval (IR) model based on possibilistic directed networks. The relevance of a document w.r.t a query is interpreted by two degrees: the necessity and the possibility. The necessity degree evaluates the extent to which a given document is relevant to a query, whereas the possibility degree evaluates the reasons of eliminating irrelevant documents. This new interpretation of relevance led us to revisit the term weighting scheme by explicitly distinguishing between informative and non-informative terms in a document. Experiments carried out on three standard TREC collections show the effectiveness of the model.     

The boundary value problem and the Jensen inequality for an entropy functional of a Markov diffusion process

The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, expressed through an additive functional of the diffusion process, with a Lagrangian, determined by the parameters of a controlled stochastic equation. These results include a minimum condition for the entropy functional and the functional's Jensen inequality, which both are useful for the solution of important mathematical and applied problems.     

Transport of biomolecules in asymmetric nanofilter arrays

We propose a theoretical model for describing the electric-field-driven migration of rod-like biomolecules in nanofilters comprising a periodic array of shallow passages connecting deep wells. The electrophoretic migration of the biomolecules is modeled as transport of point-sized Brownian particles, with the orientational degree of freedom captured by an entropy term. Using appropriate projections, the formulation dimensionality is reduced to one physical dimension, requiring minimal computation and making it ideal for device design and optimization. Our formulation is used to assess the effect of slanted well walls on the energy landscape and resulting molecule mobility. Using this approach, we show that asymmetry in the well shape, such as a well with one slanted and one vertical wall, may be used for separation using low-frequency alternating-current fields because the mobility of a biomolecule is different in the two directions of travel. Our results show that, compared to methods using direct-current fields, the proposed method remains effective at higher field strengths and can achieve comparable separation using a significantly shorter device.     

Entropy of the Binomial Field Interacting with the Two Entangled Atoms

In this paper, we investigate entropy properties of the single-mode binomial field interacting with the two entangled two-level atoms. It is found that the different initial conditions lead to the different evolutions of entropy of the binomial field.     

Ionic studies of sodium alginate isolated from Sargassum terrarium (brown algea) karachi coast with 2,1-electrolyte

Physical and chemical analysis of the polysaccharide isolated from Sargassum Terarrium (brown algae) of Karachi coast showed characteristics of the sodium alginate. Optical rotations and sulphated ash content were found and FTIR spectra showed a sharp and strong absorption band at 1600 cm^?1 representing carboxylate ion which conforms high uronic acid content of the product. The viscosities of aqueous 0.1% sodium alginate solution were measured in the presence of copper II chloride (CuCl₂). The viscosities were found to be increased with the increase in the concentration of electrolyte. Viscosities were also found affected with temperature. ‘A’ and ‘B’ coefficients of Jones–Dole equation were evaluated. The increase in positive values of ‘B’ coefficient with the rise of temperature led to conclusion that given electrolyte in 0.1% aqueous sodium alginate solution behaves as structure maker. Thermodynamic parameters regarding to activated state like energy of activation E_η, change in free energy of activation ΔG_η and change of entropy of activation ΔS_η were also evaluated. Straight-line plots of log η versus 1/T observed with positive slopes show the effect of temperature on the viscosities of solutions. Energy of activation (E_η) was found to be decreased with the rise of temperature. Change in free energy of activation (ΔG_η) was also found to be increased with increase in concentrations of electrolyte and also with rise of temperature. The values of change in entropy of activation (ΔS_η) were also calculated. Negative values of ΔS_η were found to be increased with increase in concentration of electrolyte and also with rise of temperature.     

Discrepancy of structural stability against temperature between metallic liquids and their glasses

The stability of the disordered structure in liquid or glass states could be characterized by the glass-forming ability (GFA) and thermal stability (TS), respectively. The two quantities are often, but not always, positively correlated. Here we show that the discrepancy between GFA and TS originates from the competition between entropy and enthalpy which fairly much relies on local structural characteristics. This inherent interaction and competition determines hierarchy of phase stability against temperature. As a result, the time susceptibility of GFA and temperature susceptibility of TS were derived from the time-temperature-transformation diagram, which are coincided with the above mentioned entropy-enthalpy competition perspective. Thus, the interrelationship among entropy, enthalpy and local cluster feature provides a potential resolution to design and optimize glass formers, and have implications for better understanding the nature of glass transition.     

Decoherence in quantum mechanics

We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the system’s total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.