Showing papers in "Entropy in 2007"

Design of Experiments: Useful Orthogonal Arrays for Number of Experiments from 4 to 16

Abstract: A methodology for the design of an experiment is proposed in order to find asmany schemes as possible with the maximum number of factors with different levels for thesmallest number of experimental runs. An algorithm was developed and homemadesoftware was implemented. The abilities in generation of the largest groups of orthogonalarrays were analyzed for experimental runs of 4, 6, 8, 9, 10, 12, 14, 15, and 16. The resultsshow that the proposed method permits the construction of the largest groups of orthogonalarrays with the maximum number of factors.

On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders

Abstract: Effects of the bounding solid walls are examined numerically for slow flow overregular, square arrays of circular cylinders between two parallel plates. A local magnitudeof the rate of entropy generation is used effectively to determine the flow region affected bythe presence of the solid boundary. Computed axial pressure gradients are compared to thecorresponding solution based on the Darcy-Brinkman equation for porous media in whichthe effective viscosity appears as an additional property to be determined from the flowcharacteristics. Results indicate that, between two limits of the Darcian porous medium andthe viscous flow, the magnitude of μ (the ratio of the effective viscosity to the fluid ˆviscosity) needs to be close to unity in order to satisfy the non-slip boundary conditions atthe bounding walls. Although the study deals with a specific geometric pattern of the porousstructure, it suggests a restriction on the validity of the Darcy-Brinkman equation to modelhigh porosity porous media. The non-slip condition at the bounding solid walls may beaccounted for by introducing a thin porous layer with μ = 1 near the solid walls. ˆ

A Simple Thermodynamic Analysis of Photosynthesis

Abstract: In this paper we present a comparative study of nine photosynthetic pathways bymeans of their thermodynamic performance. The comparison is made by using the thermalefficiency of light-to-chemical energy conversion and the so-called ecological criterionarising from finite-time thermodynamics. The application of both criteria leads tophotosynthesis made by metaphytes and non sulfur purple bacteria as those of bestthermodynamic performance. In spite of the simplicity of our thermodynamic approachsome insights over the low overall efficiency of photosynthesis is suggested.

A Utility-Based Approach to Some Information Measures

Abstract: We review a decision theoretic, i.e., utility-based, motivation for entropy and Kullback-Leibler relative entropy, the natural generalizations that follow, and various properties of thesegeneralized quantities. We then consider these generalized quantities in an easily interpreted spe-cial case. We show that the resulting quantities, share many of the properties of entropy andrelative entropy, such as the data processing inequality and the second law of thermodynamics.We formulate an important statistical learning problem – probability estimation – in terms of ageneralized relative entropy. The solution of this problem reflects general risk preferences via theutility function; moreover, the solution is optimal in a sense of robust absolute performance.

The Natural Philosophy of Work

Abstract: Work, by dissipative structures (DS), imposes delay on energy gradient degradation. It diverts energy flow into DS maintenance while enhancing energy degradation. DS can be viewed as tradeoffs between enhancing entropy production maximization (the maximum entropy production principle, MEP) by way of convective gradient degradation, and the need to maintain DS form, which is what mediates the convective dissipation. This tradeoff frameworked the origin of living DS. In the Big Bang, the Universe departed increasingly from an ordered state of low entropy. As a result the Second Law (locally, dS> or = 0) became an ever more powerful attractor, insuring that work could have only limited energy efficiency (utilization / throughput). That is, the ‘>’ in ‘dS > or = 0’ increased on average locally as the universe departed further from thermodynamic equilibrium. Energy efficiency becomes significant in the context of possible energy shortage, which implies embodied agency, implying in turn the possibility of some stability into the future. Energy efficiency is needed in living DS which yet serve MEP by becoming relatively less energy efficient when striving. Biodiversity multiplies modes of energy consumption, also furthering MEP by compensating for the diversion of energy flow into the maintenance of living DS. Modular (hierarchical) structure is very stable to perturbations, and also generates the variety requisite for adaptive flexibility, affording as well evolutionary access to increased adjacent possibilities. Dynamical rate separation between hierarchical levels streamlines energy flows, enhancing orderly energy gradient degradation. I conjecture that new levels are interpolated when that fosters MEP overall. Of the three phases of energy flow -- low level conduction, mid level convection, and high level explosion -- orderly convection associates with DS form, constraining moderated energy flows, and defusing potential explosions.

On the So-Called Gibbs Paradox, and on the Real Paradox

Abstract: Two versions of the so-called Gibbs paradox are discussed. Both of these areshown to be non-paradoxes. It is also shown that there is a different real paradox that emergesfrom Gibbs writings.Keywords: Gibbs ParadoxThis is a short discussion of my views on the so-called Gibbs paradox ( GP ) . The fact is that Gibbshimself never mentioned this paradox [1], and whatever is referred to as Gibbs paradox is not really aparadox at all.There are several versions of the so-called Gibbs paradox. We shall discuss here two versions of the GP and show that one arises from treating the particle classically, not recognizing the indistinguishability( ID ) of the particles, the other involves the fallacious idea that the ID of the particles is a property thatcan be changed continuously.The first paradox arises when we use the (purely) classical partition function. As is well known, theclassical PF gives the correct equation of state, the correct heat capacity and some other properties of anideal gas [2]. It fails to give the correct entropy or the chemical potential. More specifically the entropy(or better the missing information) of a system, derived from the classical partition function, does nothave the additive property, or more generally, S

Entropy of Relativistic Mono-Atomic Gas and Temperature Relativistic Transformation in Thermodynamics

Abstract: It is demonstrated that the entropy of the ideal mono-atomic gas comprising identical spherical atoms is not conserved under the Planck-Einstein like relativistic temperature transformation, as a result of the change in the number of atomic degrees of freedom. This fact supports the idea that there is no universal relativistic temperature transformation. Keywords: relativistic temperature transformation, ideal gas, entropy, degrees of freedom. PACS numbers: 05.70.-a, 95-30.Tg. Introduction The problems of relativistic thermodynamics and statistics attracted significant attention recently [1–4]. The interest to the field was boosted by modern astrophysics investigations. One of the most debated problems is the relativistic temperature transformation. The Planck-Einstein (PE) approach to the temperature transformation resulted in the well-known relation [5]: 2 0 02 11 T TcT u γ= − = (1) 2 0 02 d1d 1 dQ QcQ u γ= − = (2) where 2122( ) 1 − ⎥⎦⎤⎢⎣⎡= = − cuγ γu T and d Q are the temperature and the heat respectively. Ott in his early work concluded that the relativistic temperature transformation is at least ambiguous, because the

Distillation of a Complex Mixture. Part II: Performance Analysis of a Distillation Column Using Exergy

Abstract: To analyze the performance of the separation process, we have introduced thethermodynamic concept of exergy through the exergetic efficiency of the column. Thesimulation results show that the exergetic output is relatively low and that the producedirreversibility fluxes are distributed throughout the whole column in a non-uniform manner.They are particularly significant in the condenser, boiler and tray feed. The influence of thevarious operating parameters (temperature, concentration and irreversibility in both sectionsof the column) is also established. To emphasize the results, the relation in equation 17, ispresented graphically to evaluate the cumulative irreversibilities from the overhead to thebottom. This presentation is equivalent to the Grassmann diagram.

Second Law Analysis of a non-Newtonian Laminar Falling Liquid Film Along an Inclined Heated Plate

Abstract: The second law analysis of heat transfer of a non-Newtonian, laminar falling liquid film along an inclined heated plate is investigated. The upper surface of the liquid film is considered free and adiabatic. Velocity and temperature profiles are obtained analytically and used to compute the entropy generation number (N s ), irreversibility ratio ( ) and the Bejan number (Be) for several values of the viscous dissipation parameter (Br Ω -1 ), viscosity index (n) and the dimensionless axial distance (X). The Bejan number increases in the transverse direction and decreases as the viscous dissipation parameter (Br Ω -1 ) increases. The numerical results show that the Bejan number decreases as the viscous dissipation parameter (Br Ω -1 ), Peclet number (Pe) and the viscosity index (n) increase. Keywords: Second law, Falling liquid film, heat transfer, Non-Newtonian fluids, Bejan number. Nomenclature Α thermal diffusivity, m

On Optimization of a Non-Endorreversible Curzon-Ahlborn Cycle

Abstract: A non-endoreversible Curzon and Ahlborn cycle is analyzed by introducing a factor of non-endoreversibility. The form of power output and ecological function, and the role of this factor is discussed. The Gutkowics-Krusin, Procaccia and Ross method to build a general expression for both the power output and the ecological function for this cycle is used. A numerical analysis of these expresions is made and the results are compared with other kind of approaches found in the literature of finite time thermodynamics. Keywords: efficiency, finite time thermodynamics, non-endoreversible cycle PACS: 44.6.+k, 44.90.+c 1. Introduction As it is known the Curzon and Ahlborn cycle [1] is a model of an endoreversible engine, shown in Figure 1. The efficiency of this cycle is a bound of real engines and it is written as C T HT ηCA =1− , (1) where T C is the cold reservoir temperature and T H is the hot reservoir temperature. This endoreversible cycle is an engine in which entropy production during the exchange of heat between the system and its reservoirs of heat is only taken into account.

A Model of Time

Abstract: Based on a mathematical model of quantum measurement we derive some proper-ties of intuitive time.Keywords: Quantum Entropy, Energy, Measurement, Time.MSC 2000 Codes: 94A17, 81P151. IntroductionIn [7 ; 8] we present a model of quantum measurement which bases on the notions of decoherence andcollapse. Given an apparatus or register A , a system S and the environment E at temperature T , themeasurement process M can be thought of as being represented by the following sequence: M := A›S ! d tr E ( A›S ) ! p A ¶ ›S ¶ , ¶ 2 I: (1)The first step, d; is the decoherence of the entangled AS system and the creation of classical alterna-tives, mathematically expressed by a density matrix ‰ AS . The second step, p , is the projection or collapseto one of the eigenstates and a definite outcome. There is a fluctuation of entropy S ‰ AS connected to M .The fluctuation of entropy creates a pulse of energy whose average satisfies E 1 kTS ‰ AS where k de-notes the Boltzmann constant. The term ”measurement” is somewhat misleading in this context and wewant to replace it by ”realization” because what happenes in

Probability as a Physical Motive

Abstract: Recent theoretical progress in nonequilibrium thermodynamics, linking thephysical principle of Maximum Entropy Production (“MEP”) to the information-theoretical“MaxEnt” principle of scientific inference, together with conjectures from theoreticalphysics that there may be no fundamental causal laws but only probabilities for physicalprocesses, and from evolutionary theory that biological systems expand “the adjacentpossible” as rapidly as possible, all lend credence to the proposition that probability shouldbe recognized as a fundamental physical motive. It is further proposed that spatial order andtemporal order are two aspects of the same thing, and that this is the essence of the secondlaw of thermodynamics.

Entropy Characteristic on Harmonious Unifying Hybrid Preferential Networks

Abstract: Based on the harmonious unifying hybrid preferential model ( HUHPM ) network proposed by our group, the entropy characteristic of an un-weighted HUHPM-BA network and a weighted HUHPM-BBV network are investigated as the total hybrid ratio d/r is changed. We derive and compute the general relation of the power exponent of the degree distribution with the entropy by using the Boltzmann-Gibbs entropy ( BGS ) and the Tsallis non-extensive entropy ( S q ). It is found that the BGS decreases as d/r increases and the current of the BGS along with hybrid ratio d/r or exponent γ of power-law is in agreement between numerical simulation and theoretical analysis. The relationship between the S q and characteristic parameter q under different d/r is also given. And the S q approaches to the BGS when q →1. These results can provide a better understanding for evolution characteristic in growing complex networks and further applications in network engineering are of prospective potential.

Distillation of a Complex Mixture. Part I: High Pressure Distillation Column Analysis: Modeling and Simulation

Abstract: In this analysis, based on the bubble point method, a physical model was established clarifying the interactions (mass and heat) between the species present in the streams in circulation in the column. In order to identify the externally controlled operating parameters, the degree of freedom of the column was determined by using Gibbs phase rule. The mathematical model converted to Fortran code and based on the principles of: 1) Global and local mass conservation balance, 2) Enthalpy balance, and 3) Vapour-liquid equilibrium at each tray, was used to simulate the behavior of the column, concentration distributions, temperature and streams for each phase along the column at high pressure in each tray. The energy consumption at the condenser and the boiler was also evaluated using the Starling equation of state. Keywords: High pressure distillation, complex mixture, modeling, simulation, bubble point method. 1. Introduction Numerous methods are cited in the literature regarding the resolution of the complex mixtures distillation problem. However; the engineer often resorts to the shortcut method which enables the computation of the minimum number of trays (N

Thermodynamics of Horizons from a Dual Quantum System

Abstract: It was shown recently that, in the case of Schwarschild black hole, one can obtainthe correct thermodynamic relations by studying a model quantum system and using a partic-ular duality transformation. We study this approach further for the case a general sphericallysymmetric horizon. We show that the idea works for a general case only if we define the en-tropy S as a congruence (“observer”) dependent quantity and the energy E as the integral overthe source of the gravitational acceleration for the congruence. In fact, in this case, one recov-ers the relation S = E/2T between entropy, energy and temperature previously proposed byone of us in gr-qc/0308070. This approach also enables us to calculate the quantum correc-tions of the Bekenstein-Hawking entropy formula for all spherically symmetric horizons.

Geometric Entropy of Self-Gravitating Systems

Abstract: We shall review different approaches to the entropy of self-gravitating systems inGeneral Relativity. Then we shall discuss in detail the macroscopic approach based on a la `Clausius point of view. Recent developments will be reviewed discussing the aims as well asthe assumptions which the framework is based on.