We show by advanced electronic structure calculations that NbO 2 essentially is a Peierls-type material. After simulating the rutile as well as the body-centered tetragonal phase with the Bethe-Salpeter equation, we are able to reproduce the experimental values for the electronic properties without adding correlations. Our calculation includes only excitonic corrections and no further interactions. The principal indirect gap is between N and and is found to be 0.98 eV, the direct gap at the point amounts to 1.35 eV. We found the rutile structure to be anisotropic, with nesting vectors in the Fermi surfaces in the MAZ and X RZ planes.

The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.

No abstract

Dispersive diffusion and wave propagation seem to be unconnected and fundamentally different evolution equations. In the context of anomalous diffusion however modeling approaches based on fractional diffusion equations have been presented, which allow to build a continuous bridge between the two regimes. The transition from irreversible dispersive diffusion to reversible wave propagation shows an unexpected increase in entropy production. This seemingly paradoxical behavior of fractional diffusion is reviewed and compared to the behavior of a tree-based diffusion model.