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Heterogeneous Cattaneo-Vernotte equation connection to the noisy voter model
K Górska1, A Horzela1, D Jankov Maširević2
1Division of Theoretical Physics, Polish Academy of Sciences, H. Niewodniczański Institute of Nuclear Physics, ul. Eliasza-Radzikowskiego 152, PL 31-342 Kraków, Poland.
None:
We consider a heterogeneous diffusion equation and its corresponding generalization to the Cattaneo-Vernotte equation. It is derived by a combination of the continuity equation and the constitutive relation in various stochastic interpretations of the heterogeneous diffusion process. The heterogeneity in the system is introduced by considering a position-dependent diffusion coefficient. The exact results for the probability density function and the mean-squared displacement are provided. The limiting case of heterogeneous diffusion is analyzed in detail, and the corresponding time-averaged mean-squared displacement is calculated. From the obtained results, an ergodicity breaking is observed.
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