2013/05/10 by Amir Aghamohammadi, Amir H. Fatollahi, Mohammad Khorrami +1
Materials Science · Mathematics · Physics and Astronomy · #Binary entropy function #Entropy (arrow of time) #Entropy rate #Fractional Differential Equations Solutions #Logarithm #Material Dynamics and Properties #Mathematical analysis #Mathematics #Maximum entropy probability distribution #Physics #Principle of maximum entropy #Statistical physics #Statistics #Thermodynamics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/j.physleta.2013.05.015
published as Phys. Lett. A 377 (2013) 1677 · latex2e, 1+10 pages, no fig
openalex publication_date 2013/05/10 · arxiv created 2013/05/23 · arxiv updated 2013/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.