Fractional diffusion and entropy production

The entropy production rate for fractional diffusion processes is calculated and shows an apparently counter-intuitive increase with the transition from dissipative diffusion behaviour to reversible wave propagation. This is deduced directly from invariant and non-invariant factors of the (probability) density function, arising from a group method applied to the fractional differential equation which exists between the pure wave and diffusion equations. However, the counter-intuitive increase of the entropy production rate within the transition turns out to be a consequence of increasing quickness of processes as the wave case is approached. When this aspect is removed the entropy shows the expected decrease with the approach to the reversible wave limit.