Entropy

2100 KiB

Open AccessArticle

Analysis of the Magnetic Field Effect on Entropy Generation at Thermosolutal Convection in a Square Cavity

by Mounir Bouabid, Nejib Hidouri, Mourad Magherbi and Ammar Ben Brahim

Entropy 2011, 13(5), 1034-1054; https://doi.org/10.3390/e13051034 - 23 May 2011

Cited by 21 | Viewed by 6950

Thermosolutal convection in a square cavity filled with air and submitted to an inclined magnetic field is investigated numerically. The cavity is heated and cooled along the active walls with a mass gradient whereas the two other walls of the cavity are adiabatic and insulated. Entropy generation due to heat and mass transfer, fluid friction and magnetic effect has been determined in transient state for laminar flow by solving numerically the continuity, momentum energy and mass balance equations, using a Control Volume Finite—Element Method. The structure of the studied flows depends on four dimensionless parameters which are the Grashof number, the buoyancy ratio, the Hartman number and the inclination angle. The results show that the magnetic field parameter has a retarding effect on the flow in the cavity and this lead to a decrease of entropy generation, Temperature and concentration decrease with increasing value of the magnetic field parameter. Full article

(This article belongs to the Special Issue Entropy Generation Minimization)

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2107 KiB

Open AccessArticle

Entropy Generation at Natural Convection in an Inclined Rectangular Cavity

by Mounir Bouabid, Mourad Magherbi, Nejib Hidouri and Ammar Ben Brahim

Entropy 2011, 13(5), 1020-1033; https://doi.org/10.3390/e13051020 - 23 May 2011

Cited by 46 | Viewed by 8099

Abstract

Natural convection in an inclined rectangular cavity filled with air is numerically investigated. The cavity is heated and cooled along the active walls whereas the two other walls of the cavity are adiabatic. Entropy generation due to heat transfer and fluid friction has been determined in transient state for laminar natural convection by solving numerically: the continuity, momentum and energy equations, using a Control Volume Finite Element Method. The structure of the studied flows depends on four dimensionless parameters which are: the thermal Grashof number, the inclination angle, the irreversibility distribution ratio and the aspect ratio of the cavity. The obtained results show that entropy generation tends towards asymptotic values for lower thermal Grashof number values, whereas it takes an oscillative behavior for higher values of thermal Grashof number. Transient entropy generation increases towards a maximum value, then decreases asymptotically to a constant value that depends on aspect ratio of the enclosure. Entropy generation increases with the increase of thermal Grashof number, irreversibility distribution ratio and aspect ratio of the cavity. Bejan number is used to measure the predominance of either thermal or viscous irreversibility. At local level, irreversibility charts show that entropy generation is mainly localized on bottom corner of the left heated wall and upper corner of the right cooled wall. Full article

(This article belongs to the Special Issue Entropy Generation Minimization)

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370 KiB

Open AccessArticle

The Michaelis-Menten-Stueckelberg Theorem

by Alexander N. Gorban and Muhammad Shahzad

Entropy 2011, 13(5), 966-1019; https://doi.org/10.3390/e13050966 - 20 May 2011

Cited by 54 | Viewed by 10658

Abstract

We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events). This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework. Full article

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212 KiB

Open AccessArticle

The Decoherence of the Electron Spin and Meta-Stability of ¹³C Nuclear Spins in Diamond

by Peter Crompton

Entropy 2011, 13(5), 949-965; https://doi.org/10.3390/e13050949 - 05 May 2011

Cited by 1 | Viewed by 6599

Abstract

Following the recent successful experimental manipulation of entangled ¹³C atoms on the surface of Diamond, we calculate the decoherence of the electron spin in Nitrogen Vacancy NV centers of Diamond via a nonperturbative treatment of the time-dependent Greens function of a Central-Spin model in order to identify the Replica Symmetry Breaking mechanism associated with intersystem mixing between the m_s = 0 sublevel of the ³A₂ and ¹A₁ states of the NV⁻ centers, which we identify as mediated via the meta-stability of 13C nuclei bath processes in our calculations. Rather than the standard exciton-based calculation scheme used for quantum dots, we argue that a new scheme is needed to formally treat the Replica Symmetry Breaking of the ³A₂ → ³E excitations of the NV⁻ centers, which we define by extending the existing Generalized Master Equation formalism via the use of fractional time derivatives. Our calculations allow us to accurately quantify the dangerously irrelevant scaling associated with the Replica Symmetry Breaking and provide an explanation for the experimentally observed room temperature stability of Diamond for Quantum Computing applications. Full article

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91 KiB

Open AccessArticle

Is Gravity an Entropic Force?

by Shan Gao

Entropy 2011, 13(5), 936-948; https://doi.org/10.3390/e13050936 - 28 Apr 2011

Cited by 34 | Viewed by 11220

Abstract

The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic force is debatable. It is shown that there is no convincing analogy between gravity and entropic force in Verlinde’s example. Neither holographic screen nor test particle satisfies all requirements for the existence of entropic force in a thermodynamics system. Furthermore, we show that the entropy increase of the screen is not caused by its statistical tendency to increase entropy as required by the existence of entropic force, but in fact caused by gravity. Therefore, Verlinde’s argument for the entropic origin of gravity is problematic. In addition, we argue that the existence of a minimum size of spacetime, together with the Heisenberg uncertainty principle in quantum theory, may imply the fundamental existence of gravity as a geometric property of spacetime. This may provide a further support for the conclusion that gravity is not an entropic force. Full article

(This article belongs to the Special Issue Black Hole Thermodynamics)

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Entropy, Volume 13, Issue 5 (May 2011) – 5 articles , Pages 936-1054

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