Entropy as a measure of diffusion |
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Authors: | Amir Aghamohammadi Amir H. Fatollahi Mohammad Khorrami Ahmad Shariati |
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Affiliation: | Department of Physics, Alzahra University, Tehran 19938-93973, Iran |
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Abstract: | 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. |
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Keywords: | Diffusion equation Anomalous diffusion Fractional derivative |
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