Entropy as a measure of diffusion

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For system...

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Bibliographic Details
Published in:Physics letters. A 2013-10, Vol.377 (28-30), p.1677-1681
Main Authors: Aghamohammadi, Amir, Fatollahi, Amir H., Khorrami, Mohammad, Shariati, Ahmad
Format: Article
Language:English
Subjects:
Anomalous diffusion
Constants
Density
Diffusion
Diffusion equation
Diffusion rate
Entropy
Fractional derivative
Invariants
Solid state physics
Variance
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Summary:The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions. •Entropy was introduced as a tool to study how fast the diffusion in a system occurs.•Systems with ill-defined variance evolution but well-defined entropy are introduced.•Two regimes as long-time behavior of entropy: exponential and logarithm of time.•Some anomalous diffusions and the behavior of their entropies were studied.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2013.05.015