Shear-driven finite-velocity diffusion and its generalization

We consider shear-driven finite-velocity diffusion, both normal and anomalous. In the macroscopic description, this leads to a telegrapher's or Cattaneo-like equation. We analyze the probability density function, and the corresponding moments are obtained analytically. We show that the system exhibits a characteristic crossover of the anomalous dynamics. We also explore corresponding processes under stochastic resetting and find that the systems reach non-equilibrium stationary states in the long time limit that also results in saturation of the evolution of the corresponding mean squared displacement, variance, skewness, and kurtosis.