The new non-Markovian diffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo--Maxwell diffusion equation with taking into account the space-time nonlocality are obtained. Dispersion relations for the Cattaneo--Maxwell-type diffusion equation with taking into account the space-time nonlocality in fractional derivatives are found. The frequency spectrum, phase and group velocities are calculated. It is shown that it has a wave behavior with discontinuities, which are also manifested in behavior of the phase velocity.
nonequilibrium statistical operator
The new non-Markovian electrodiffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo-type diffusion equation with taking into account fractality of space-time are obtained. Different models of the frequency dependence of memory functions, which lead to known diffusion equations with fractality of space-time and their generalizations are considered.
We propose a statistical theory of classical-quantum description of electro-diffusion processes of intercalation in "electrolyte – electrode" system. Using the nonequilibrium statistical operator method the generalized transport equations of Nernst-Planck type for ions and electrons in the "electrolyte – electrode" system are obtained. These equations take into account time memory effects and spatial heterogeneity. Within a classical description an analytical calculation of spatially inhomogeneous diffusion coefficients for ions is carried out.