Jet bundle technique, Lie Bäcklund vector fields and diffusion equations

2005 ◽  
pp. 130-132 ◽  
Author(s):  
W. -H. Steeb ◽  
W. Strampp
Keyword(s):  
Vector Fields ◽  
Diffusion Equations ◽  
Jet Bundle ◽  
And Diffusion

Adolf Fick and Diffusion Equations

2006 ◽  
Vol 249 ◽  
pp. 1-6 ◽  
Author(s):  
Jean Philibert
Keyword(s):  
Diffusion Equations ◽  
Seminal Paper ◽  
And Diffusion

After some biographical notes, Fick’s 1855 seminal paper is analysed and the contributions of Stefan and Roberts-Austen are briefly mentioned.

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.

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