Investigations on exergy resources are important from the point of energy sustainability. In the presented study an energy and exergy analysis of the operating biomass and natural gas boilers at the University of Idaho (UI) district energy plant is conducted. Exergy flows through the components of the steam cycle associated with the biomass boiler are quantified to identify major sources of exergy destruction in the district heating system. It is found that the biomass boiler has reduced energy and exergy efficiency compared to the natural gas boilers. Thermal efficiency varies from 76% to 85%, while exergy efficiency is significantly lower at 24% to 27% for all the boilers.  Exergy accounting reveals that the biomass boiler and furnace account for the greatest exergy destruction, at approximately 68% of the exergy provided by the fuel. Steam use on campus represents about 6% of exergy losses while the pressure reducer is responsible for 3.5%.

After the 2008 financial collapse, (Kritzman et al 2011) introduced the now popular measure of implied systemic risk called the absorption ratio.  This statistic is constructed from a fixed number of eigenvectors, and measures how closely the economy’s markets are coupled. The more closely financial markets are coupled the more susceptible they are to systemic collapse.  (Parker 2017) utilized information theory to develop the concept of the entropic yield curve.  From this equation, the implied information processing ratio or entropic efficiency of the economy can be derived.  This entropic measure can also be useful in predicting economic downturns. In the current work, the relationship between these two ratios is explored.

Liquid impinging jet on the bottom of the annular cavity is the typical case in the process industry. The jet can impact on the bottom center or its peripheral section. The profiled annular cylindrical cavity with the installed electricity heater source investigated in this paper. Within the profiled cavity generate thermal contact irreversibility and liquid drag irreversibility. By analytical modeling and experimental verification a valid model of the entropy generation established for both states. The results show that the total entropy between the liquid and bottom is many times greater for the case of the central jet impingement. Within the annular vertical walls are locations maximum or minimum of entropy. The effectiveness of the liquid heating for the central impact is greater in the peripheral impact of liquid. The method and the results got are a basis for optimizing  profiled cavity at various optimization geometry parameters. The optimal annular cavity geometry exists for which the balance between thermal irreversibility and liquid drag irreversibility leads to the total minimum rate of entropy generation for an annular cavity.

In nonequilibrium processes, work extraction from a system is subject to random fluctuations associated with the statistical distribution prescribed by its environment. The probability of extracting work above a given arbitrary threshold can be a measure of restriction imposed by experimental circumstances. We present a lower bound for the probability when the work value lies in a finite range. For the case of unrestricted maximum work, the lower bound gets larger as the free energy difference between initial and final states becomes larger. We point out also that an upper bound previously reported in the literature is a direct consequence of the well-known second mean value theorem for definite integrals.

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a human head in the space. The applications range from structural biology, computer vision, medical imaging to archeology. We focus on the to selection of an appropriate measurement of distance among observations with the aim of obtaining an unsupervised classification of shapes.

Data from a shape are often realized as a set of representative points, called landmarks. For planar shapes, we assume that each landmark is modeled via a bivariate Gaussian, where the means capture uncertainties that arise in landmarks placement and the variances the natural variability across the population of shapes.

At first we consider the Fisher-Rao metric as a Riemannian metric on the Statistical Manifold of the Gaussian distributions. The induced geodesic-distance is related with the minimization of information in the Fisher sense and we can use it to discriminate shapes.  Another suitable distance is the Wasserstein distance, which is induced by a Riemannian metric and is related with the minimal transportation cost.

In this work,  a simulation study is conducted in order to make a comparison between the Wasserstein and the Fisher-Rao metrics when used in shapes clustering.

Genes are certain regions of the deoxyribonucleic acid (DNA), which is the hereditary material of the biological cells.  They encode for the synthesis of proteins.  Both proteins and DNA are polymeric macromolecules that are formed up of unique combinations of their respective building blocks.  Each of these building blocks is a residue and the residue-wise information content of the DNA that is encoding a certain length of protein is assumed to be inherently related to that in the protein.  Here, it is aimed to present a method that involves information communication theory, to relate the residue-wise information contents of the DNA and protein molecules.  Through information communication theory, information content of a polymeric macromolecule can be calculated in bits, by multiplying the number of building blocks that encompasses the entire length of the macromolecule with the Shannon’s entropy of each building block.  Shannon’s entropy of each building block would be determined through the degree of variation in the number of those units, by assuming equal propensity of the presence of each type of building block, at every position along the entire length of the polymeric macromolecule in question.  If this approach is applied to a protein of specific size and the DNA that would be encoding the same length of protein, there is seemingly much lower residue-based information amount in the protein.  This decrease can be eliminated by implementation of a new parameter in the calculation and/or through a new formulization of the calculation of the information amount of proteins.

The tendency of the entropy of isolated to increase is considered to be directly linked to the direction of the flow of time. This raises the question whether a quantitative relation can be established such that a time interval can be measured by measuring entropy change and vice versa. The existence or absence of such a link also calls for further consideration of the nature of time. Prigogine argued that the true nature of time can only be discovered by investigating this phenomenon using scientific and philosophical methods. If this is true, then ongoing debates in the metaphysics of time and progress in the scientific study of entropy can be brought together to shed light on this fascinating but elusive concept. In this paper, starting from my recent modified definition of entropy change as a non-dimensional measure of energy change, a direct link between entropy and time duration is presented. It draws from steady energy transfer processes such as heat transfer and shows that a measure of time can be found to be associated with a measure of entropy change. In the absence of other driving forces, the passage of time in an isolated system can therefore be tracked with a well calibrated entropy change meter. When other forces are allowed to interfere and there is no external point from which the system can be considered to be isolated, then the measure of time is non-monotonous since an isolated system can be restored to an earlier state of non-equilibrium.

Multiple equilibria of objects with several equivalent binding, docking, coupling, or adsorption sites for neutral or charged species play an important role in all fields of chemistry, including systems with interface dominated structures and functions. The influence of entropy in multiple equilibria can be dominant. We have analyzed them by studying the particle distribution for the conditions that the binding enthalpy of the species is the same for all sites and independent of those that are already bonded. This delivers information on the evolution of the entropy as the reaction proceeds. The validity of the results is independent of the nature and the strength of the binding. The results are relevant for analyzing and interpreting experimental data: e.g. acid-base, ligand exchange or ion exchange reactions, adsorption of species on a surface and insertion of charged or neutral guests into the cavities of microporous and mesoporous hosts. They are also important for understanding observations and planning the synthesis of new host-guest composites. The quantitative link between the description of multiple equilibria and Langmuir’s isotherm was found to provide new insight.^[1]

We now investigate systems with two different types of sites, for the conditions that the binding enthalpy of the species is the same for each type of sites and independent of those that are already bonded, by analyzing them using the particle distribution theory as described in ref. [1], for each type of sites separately. Procedure and results are exemplified for an X_m{AB}X_n system with m=0,1,2,3 and n=0,1,2. A numerical analysis of experimental data for system with 5 different types of sites has been carried out previously and has allowed to correct earlier reports on the reaction entropy of silver zeolite A.^[2] We now improve the physical insight by using a theoretical description.

[1] G. Calzaferri, PhysChemChemPhys, 19, 2017, 10611-10621.

[2] M. Meyer, C. Leiggener, G. Calzaferri, ChemPhysChem, 6, 2005, 1071-1080.

Modfied entropies have been extensively considered in the literature [1]. Among the most well known are the Rényi entropy [2] and the Havdra-Charvát [3] and Tsallis entropy [4]. All these depend on one or several parameters.

 By means of a modification to Superstatistics [5], one of the authors (O. Obregón) has proposed generalized entropies that depend only on the probability [6, 7] and by generalizing the Replica trick [8] the entropies that correspond to the von Neumann entropy can also be found [7]. There are three entropies  S_I = k Σ^Ω_l=1 (1−p_l ^pl ), S_II = kΣ ^Ω_l=1 (p_l^−pl − 1),  and their linear combination    S_III = kΣ ^Ω_l=1 (p_l ^−pl −p_l ^pl ) / 2..

It is interesting to notice that the expansion in series of these entropies having as a first term S= −kΣ ^Ω_l=1 p_l ln p_l   in the parameter  X_l ≡ p_l ln pl ≤ 1  cover, up to the first terms, any other expansion of any other possible function in X_l, one would want to propose as another entropy. The diference will be on the constants that multiply each of the terms in these expansions, but these small correction terms to the usual Boltzmann-Gibbs or Shannon entropies will be of the same order of magnitude for any possible expanded function. Then the three proposed entropies in [6,7] are the only possible generalizations of the Boltzmann-Gibbs or Shannon entropies that depend only of the probability.

 This work will deal with the analysis of the first two generalized entropies and will propose and deduce their associated quantum statistics; namely Bose-Einstein and Fermi-Dirac. The results will be compared with the standard ones and those due to the entropies in [3, 4].

[1] M.D. Esteban, D. Morales, A summary on entropy statistics, Kybernetika V 31, No. 4, 337-347 (1995).

[2] A. Rényi, Probability Theory, North Holland, Amsterdam, (1970).

[3] J.Havdra, F. Charvát, Quantification method of classification processes. Concept entropy, Kybernetika V. 3, No. 1, 30-35, (1967).

[4] C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, Journal of Statistics Physiscs. 52, 479-487 (1988).

[5] C. Beck and E. G. D. Cohen, Physica A 322, 267 (2003).

[6] O. Obregón, Entropy 12 (9), 2067 (2010).

[7] O. Obregón, Generalized information and entanglement entropy, gravitation and holography, Int. J. Mod. Phys. A. Vol. 30, No. 16 (2015).

[8] P. Calebrese and J. Cardy, J. Stat. Mech. Theory Exp. 2004, 06002 (2014).

With the rapid depletion of fossils fuels, scope for renewable energy like solar energy is huge. The efficiency of photovoltaic cells to convert the solar energy into electricity drops with the rise in temperature due to increased resistance. Thus improving the efficiency by lowering the thermal resistance and allowing the cooling fluid (air/water) to flow through photovoltaic thermal (PVT) system is an attractive engineering problem. In the present study, performance analysis of single glazed solar PVT air collector on the basis of energy and exergy has been analyzed for the climatic conditions of Silchar, India for the month of May, 2017. An analytical model is developed to evaluate the hourly variation of PV cell temperature, cell efficiency, useful thermal heat gain, useful electrical heat gain, energy efficiency and exergy efficiency PVT system. Results depict that efficiency of PV cell decreases with the increase in temperature, and a maximum efficiency of 14.6% for the PV module is found. Out of total useful heat output, electrical heat output contributes 67% while the rest is thermal heat output. Further, magnitude of both the heat output is found to increase with the solar radiation and the maximum is observed at around 1230 hrs. Trend of both energy and exergy efficiency is similar except the magnitude. Maximum efficiency observed to be 69% and 16.5% for energy and exergy respectively.