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Approach to nonequilibrium: From anomalous to Brownian diffusion via non-Gaussianity
I G Marchenko1,2, I I Marchenko3, J Łuczka2
1NSC "Kharkiv Institute of Physics and Technology," Kharkiv 61108, Ukraine.
This study reveals that a Brownian particle in a periodic potential driven by a periodic force exhibits non-Gaussian diffusion. Non-Gaussianity correlates with transient anomalous diffusion, even when long-time diffusion appears Brownian.
Area of Science:
- Statistical physics
- Complex systems
- Nonlinear dynamics
Background:
- Experimental advances like single particle tracking enable analysis of systems approaching equilibrium.
- Processes at finite timescales can differ significantly from equilibrium behavior.
Purpose of the Study:
- To investigate the approach to nonequilibrium in a model system.
- To analyze the diffusion process of a Brownian particle in a spatially periodic potential driven by an external time-periodic force.
Main Methods:
- Modeling a Brownian particle in a periodic potential subjected to a time-periodic driving force.
- Monitoring the diffusion process and analyzing the particle displacement distribution over time.
Main Results:
- Excess kurtosis, indicating Gaussianity, shows non-monotonic evolution: negative (platykurtic), then positive (leptokurtic), finally decaying to zero (mesokurtic).
- Despite long-time Brownian behavior, diffusion remains non-Gaussian.
- A correlation is found between non-Gaussian displacement distributions and transient anomalous diffusion at finite timescales.
Conclusions:
- The approach to nonequilibrium in driven systems can exhibit complex, non-monotonic behavior.
- Non-Gaussian diffusion is a key feature of this driven Brownian system, linked to transient anomalous diffusion.
- Understanding these nonequilibrium dynamics is crucial for interpreting experimental data from similar systems.
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