Tsallis entropy production for diffusion on the diluted hypercube

We investigate the production of Tsallis entropy for the probability distribution of random walkers on a hypercube with a fraction p of allowed sites. We consider two regimes, p=1 and from p=12 until the percolation limit pc. In the first regime, we show that the entropy rate can be obtained from the Boltzmann–Gibbs–Shannon entropy time evolution. On the second regime, the same numerical experiments indicate a trivial limit for this quantity, while by measuring the production of Tsallis entropy for different q values there exists a particular value for the entropic index q that adequately describe the relaxation. These results are compared to similar numerical experiments performed with non-linear maps and indicate an analogy between the phase space of both systems.