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Updated: Aug 9, 2026
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Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
Published on: January 16, 2016
Do strange kinetics imply unusual thermodynamics?
I M Sokolov1, J Klafter, A Blumen
1Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany.
Summary
This study introduces a fractional Fokker-Planck equation for Lévy flights, revealing regular exponential relaxation to Boltzmann equilibrium under external fields, unlike subdiffusive cases.
Area of Science:
- Physics
- Statistical Mechanics
- Anomalous Transport
Background:
- Lévy flights exhibit anomalous transport phenomena.
- External fields influence particle dynamics.
- Fractional Fokker-Planck equations model anomalous diffusion.
Purpose of the Study:
- Introduce a fractional Fokker-Planck equation (FFPE) for Lévy flights with external fields.
- Analyze the relaxation dynamics towards equilibrium.
- Compare Lévy-flight FFPE with subdiffusive FFPE.
Main Methods:
- Derivation of FFPE using subordination of random processes.
- Analysis of relaxation behavior in the presence of a potential.
- Comparison of relaxation times and distributions.
Main Results:
- The Lévy-flight FFPE shows regular exponential relaxation to Boltzmann equilibrium.
- Subdiffusive FFPE exhibits nonexponential Mittag-Leffler relaxation.
- Both models reach Boltzmann equilibrium without modifying thermodynamics.
Conclusions:
- The derived FFPE accurately describes anomalous transport in Lévy flights.
- The presence of a potential leads to predictable equilibrium states.
- Strange kinetics, characterized by anomalous transport, still converge to standard thermodynamic equilibrium.
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