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Lévy diffusion as an effect of sporadic randomness
M Bologna1, P Grigolini, J Riccardi
1Center for Nonlinear Science, University of North Texas, P.O. Box 5368, Denton, Texas 76203, USA.
Summary
Lévy diffusion processes, a non-ordinary statistical mechanics, can be dynamically derived. This requires a random source in microscopic dynamics and accounting for memory erasure in theoretical treatments.
Area of Science:
- Statistical mechanics
- Non-ordinary processes
Background:
- Lévy diffusion processes are a type of non-ordinary statistical mechanics.
- These processes conventionally rely on the Markov property.
Purpose of the Study:
- To explore the dynamic derivation of Lévy diffusion processes.
- To identify the conditions necessary for such a derivation.
Main Methods:
- Investigating the theoretical underpinnings of Lévy diffusion.
- Analyzing the role of microscopic dynamics and memory erasure.
Main Results:
- Dynamic derivation is possible under specific conditions.
- A source of randomness in microscopic dynamics is essential.
- Proper theoretical treatment of memory erasure is a prerequisite.
Conclusions:
- Lévy diffusion processes can be dynamically derived.
- The derivation is contingent upon incorporating randomness and managing memory effects.