Transport equations for distillation of ethanol and water from the entropy production rate

2003 ◽  
Vol 58 (7) ◽  
pp. 1147-1161 ◽  
Author(s):  
Signe Kjelstrup ◽  
Gelein M.de Koeijer
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Transport Equations ◽  
Entropy Production Rate

scholarly journals On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 204 ◽  
Author(s):  
Shu-Nan Li ◽  
Bing-Yang Cao
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Power Series Expansion ◽  
Irreversible Thermodynamics ◽  
Entropy Density ◽  
Transport Equations ◽  
Entropy Production Rate ◽  
Boltzmann Transport ◽  
Relaxation Time Approximation ◽  
Entropy Flux

Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects.

scholarly journals Entropy Production Rate for Avascular Tumor Growth

2011 ◽  
Vol 02 (06) ◽  
pp. 615-620 ◽  
Author(s):  
Elena Izquierdo-Kulich ◽  
Esther Alonso-Becerra ◽  
José M Nieto-Villar
Keyword(s):  
Tumor Growth ◽  
Entropy Production ◽  
Production Rate ◽  
Entropy Production Rate ◽  
Avascular Tumor

scholarly journals Measurement of entropy production rate in compressible turbulence

2006 ◽  
Vol 76 (4) ◽  
pp. 595-601 ◽  
Author(s):  
M. M Bandi ◽  
W. I Goldburg ◽  
J. R Cressman
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Compressible Turbulence ◽  
Entropy Production Rate

scholarly journals Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 881 ◽  
Author(s):  
Karl Hoffmann ◽  
Kathrin Kulmus ◽  
Christopher Essex ◽  
Janett Prehl
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Irreversible Processes ◽  
Entropy Production Rate ◽  
Continuous Space ◽  
One Dimensional ◽  
Fractional Diffusion Equations ◽  
And Diffusion

The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.

scholarly journals Testing the Steady-State Fluctuation Relation in the Solar Photospheric Convection

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 716
Author(s):  
Giorgio Viavattene ◽  
Giuseppe Consolini ◽  
Luca Giovannelli ◽  
Francesco Berrilli ◽  
Dario Del Moro ◽  
...  
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Production Rate ◽  
Local Level ◽  
Entropy Production Rate ◽  
Quasi Steady State ◽  
The Sun ◽  
Statistical Features ◽  
Local Entropy ◽  
Fluctuation Relation

The turbulent thermal convection on the Sun is an example of an irreversible non-equilibrium phenomenon in a quasi-steady state characterized by a continuous entropy production rate. Here, the statistical features of a proxy of the local entropy production rate, in solar quiet regions at different timescales, are investigated and compared with the symmetry conjecture of the steady-state fluctuation theorem by Gallavotti and Cohen. Our results show that solar turbulent convection satisfies the symmetries predicted by the fluctuation relation of the Gallavotti and Cohen theorem at a local level.

Entropy production rate as a constraint for collisionless fluid closures

2006 ◽  
Author(s):  
E. Fleurence ◽  
Y. Sarazin ◽  
X. Garbet ◽  
G. Dif-Pradalier ◽  
Ph. Ghendrih ◽  
...  
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Entropy Production Rate
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