The entropy production paradox for fractional master equations

Kulmus, Kathrin; Essex, Christopher; Prehl, Janett; Hoffmann, Karl Heinz

doi:10.1016/j.physa.2019.03.114

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2023

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When transiting from the dissipative behavior (β = 1) to the reversible wave propagation (β = 2), a decrease in the entropy production was expected, but the reverse was observed. This phenomenon was treated in many studies, trying to find a suitable interpretation and understanding the possible underlying physical reasons [23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

An Entropy Paradox Free Fractional Diffusion Equation

Ortigueira¹

2021

Fractal Fract

View full text Add to dashboard Cite

A new look at the fractional diffusion equation was done. Using the unified fractional derivative, a new formulation was proposed, and the equation was solved for three different order cases: neutral, dominant time, and dominant space. The solutions were expressed by generalizations of classic formulae used for the stable distributions. The entropy paradox problem was studied and clarified through the Rényi entropy: in the extreme wave regime the entropy is −∞. In passing, Tsallis and Rényi entropies for stable distributions are introduced and exemplified.

show abstract

Section: Introductionmentioning

confidence: 99%

An Entropy Paradox Free Fractional Diffusion Equation

Ortigueira¹

2021

Fractal Fract

View full text Add to dashboard Cite

show abstract

The entropy production paradox for fractional diffusion

Hoffmann

Essex

Prehl

et al. 2023

Journal of Non-Equilibrium Thermodynamics

View full text Add to dashboard Cite

Dispersive diffusion and wave propagation seem to be unconnected and fundamentally different evolution equations. In the context of anomalous diffusion however modeling approaches based on fractional diffusion equations have been presented, which allow to build a continuous bridge between the two regimes. The transition from irreversible dispersive diffusion to reversible wave propagation shows an unexpected increase in entropy production. This seemingly paradoxical behavior of fractional diffusion is reviewed and compared to the behavior of a tree-based diffusion model.

show abstract

The entropy production paradox for fractional master equations

Cited by 2 publications

References 20 publications

An Entropy Paradox Free Fractional Diffusion Equation

An Entropy Paradox Free Fractional Diffusion Equation

The entropy production paradox for fractional diffusion

Contact Info

Product

Resources

About