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Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime.
Karl Heinz Hoffmann1, Kathrin Kulmus1, Christopher Essex2
1Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany.
The entropy production paradox reveals that entropy production unexpectedly increases when transitioning from irreversible diffusion to reversible wave equations. This study generalizes this counterintuitive finding to fractional diffusion on finite chains.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Non-equilibrium systems
Background:
- Entropy production rate quantifies process irreversibility.
- Reversible processes typically exhibit zero entropy production.
- Fractional diffusion equations bridge diffusion and wave equations.
Purpose of the Study:
- Investigate the entropy production paradox in fractional diffusion.
- Extend the paradox to time-fractional diffusion on finite chains.
- Analyze the behavior of Shannon, Tsallis, and Renyi entropies.
Main Methods:
- Utilized fractional master equations for time-fractional diffusion.
- Analyzed processes on a finite chain of points.
- Reviewed existing results for continuous space models.
Main Results:
- The entropy production paradox is generalized to discrete finite chains.
- The non-intuitive increase in entropy production persists in this generalized model.
- The study confirms the paradox for various entropy measures.
Conclusions:
- Fractional diffusion on finite chains exhibits the entropy production paradox.
- This finding challenges conventional understanding of irreversibility limits.
- The research expands the scope of the entropy production paradox.
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