Comment on “Generalized exclusion processes: Transport coefficients”

In a recent paper, Arita et al. [Phys. Rev. E 90, 052108 (2014)] consider the transport properties of a class of generalized exclusion processes. Analytical expressions for the transport-diffusion coefficient are derived by ignoring correlations. It is claimed that these expressions become exact in the hydrodynamic limit. In this Comment, we point out that (i) the influence of correlations upon the diffusion does not vanish in the hydrodynamic limit, and (ii) the expressions for the self- and transport diffusion derived by Arita et al. are special cases of results derived in Becker et al. [Phys. Rev. Lett. 111, 110601 (2013)].

Figure 1

Transport diffusion $D_2$ in one dimension as a function of $d\rho$, for $L_x=20$ and $\rho =1$.

Figure 2

Transport diffusion $D_2$ in one dimension as a function of $L_x$, for $\rho =1$ and $d\rho =0.1$. Value at $L_x=1$ is calculated analytically.

Figure 3

Transport diffusion $D_2$ in two dimensions as a function of $L_y$, for $d\rho =0.1, \rho =1$, and $L_x=20$. Periodic boundary conditions are imposed in the $y$ direction.

Figure 4

Transport diffusion $D_2$ in one, two, and three dimensions, for $\rho =1, d\rho =0.1, L_x=20$, and $L_y=L_z=3$. Periodic boundary conditions are imposed in the $y$ and $z$ directions. The inset shows the same data plotted as a function of $1/d$, together with a $1/d$ fit (obtained with Mathematica).

Figure 5

Transport diffusion $D_2\left(\rho \right)$ in one dimension for $L_x=50$ and $d\rho =0.18$.