Figure 9.

Entropy production of a random walk on a one-dimensional lattice (RW on $\mathbb{Z}$), for symmetric and asymmetric hopping rates, as a function of time, Equation (82) (solid lines). The asymptotic behaviour at large t, Equation (83) (dotted lines), decays algebraically in the symmetric case ($r=\ell$) and converges to a positive constant in the asymmetric case ($r\ne \ell$).