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Entropy, Volume 7, Issue 2 (June 2005), Pages 122-171

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Research

Open AccessArticle Basis of Local Approach in Classical Statistical Mechanics
Entropy 2005, 7(2), 122-133; doi:10.3390/e7020122
Received: 14 January 2005 / Accepted: 25 April 2005 / Published: 29 April 2005
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Abstract
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are obtained as well as the [...] Read more.
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are obtained as well as the simplest solution of these equations representing the quasi-local distribution with the temperature pattern being assigned. Unlike the Gibbs's distribution, the energy of interaction with surrounding particles appears in the distribution function, which make possible both evolution in the equilibrium case and fluctuations in the non-equilibrium one. The expression for local entropy is obtained. The derivation of hydrodynamic equations from Boltzmann equation has been analyzed. The hydrodynamic equations obtained from Boltzmann equation were shown to be equations for ideal liquid. Reasons for stochastic description in deterministic Hamilton's systems, conditions of applicability of Poincare's recurrence theorem as well as the problem of irreversibility have been considered. Full article
Open AccessArticle On the Entropy Production Due to Explosion in Seawater
Entropy 2005, 7(2), 134-147; doi:10.3390/e7020134
Received: 7 March 2005 / Accepted: 10 May 2005 / Published: 12 May 2005
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Abstract
The change in entropy is calculated due to propagation of blast waves, produced by the explosion of spherical charge in sea water, using the energy hypothesis of Thomas. The release of energy is considered as instantaneous and the gravitation of earth is [...] Read more.
The change in entropy is calculated due to propagation of blast waves, produced by the explosion of spherical charge in sea water, using the energy hypothesis of Thomas. The release of energy is considered as instantaneous and the gravitation of earth is taken into account, assuming the earth to be a sphere of uniform density. For the sake of simplicity, effect of rotation of the earth is not considered. The explosion is considered at different depths. It has been found that the change in entropy of water decreases at different radial points, as the shock moves away from the point of explosion. Explosion occurred at larger depths, produces a smaller change in entropy of water, then the explosion of same energy, at smaller depths. Directional dependence of entropy production and the motion of the shock are also studied. It has been found that, entropy production is larger in upward motion of the underwater shock. However the shock velocity increases in downward direction. Full article
Open AccessArticle Second Law Analysis of Laminar Flow In A Channel Filled With Saturated Porous Media
Entropy 2005, 7(2), 148-160; doi:10.3390/e7020148
Received: 10 March 2005 / Accepted: 16 May 2005 / Published: 19 May 2005
Cited by 17 | PDF Full-text (103 KB)
Abstract
The entropy generation rate in a laminar flow through a channel filled with saturated porous media is investigated. The upper surface of the channel is adiabatic and the lower wall is assumed to have a constant heat flux. The Brinkman model is employed. Velocity and temperature profiles are obtained for large Darcy number (Da) and used to obtain the entropy generation number and the irreversibility ratio. Generally, our result shows that heat transfer irreversibility dominates over fluid friction irreversibility (i.e. 0 < ø < 1), and viscous dissipation has no effect on the entropy generation rate at the centerline of the channel. Full article
Open AccessArticle On the Linear Combination of Exponential and Gamma Random Variables
Entropy 2005, 7(2), 161-171; doi:10.3390/e7020161
Received: 27 January 2005 / Accepted: 13 June 2005 / Published: 14 June 2005
Cited by 5 | PDF Full-text (158 KB)
Abstract
The exact distribution of the linear combination α X + β Y is derived when X and Y are exponential and gamma random variables distributed independently of each other. A measure of entropy of the linear combination is investigated. We also provide [...] Read more.
The exact distribution of the linear combination α X + β Y is derived when X and Y are exponential and gamma random variables distributed independently of each other. A measure of entropy of the linear combination is investigated. We also provide computer programs for generating tabulations of the percentage points associated with the linear combination. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing and other areas of computer science. Full article

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