Comment on “Generalized exclusion processes: Transport coefficients”

Abstract

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 [Phys. Rev. Lett. 111, 110601 (2013)].

Variational calculation of transport coefficients in diffusive lattice gases

“…( 34). This prediction was in good agreement with Monte Carlo simulations, but further investigations [35,36] of the 2-GEP revealed a discrepancy between the prediction and the actual value. The above approach shows how to improve this approximation in a systematic manner.…”

“…It is also possible to obtain an explicit form of D 0 as a function of ρ by substituting ( 22) into (35). We present D 0 in two cases.…”

Reply to “Comment on ‘Generalized exclusion processes: Transport coefficients’ ”

“…The numerical results of Ref. [1] and our simulations (Fig. 1) show that the perturbation approach does not lead to the correct analytical results for the GEP(2).…”

“…For the class of generalized exclusion processes which we studied [2] simulation results were indeed very close to the predictions by perturbative calculation. The comment [1] by Becker et al prompted us to perform more simulations and to analyze our results more carefully.…”

“…They performed simulations for various system sizes L and various density differences δρ between the boundary reservoirs. In order to extract D(ρ) from simulations they needed to take [1] two limits: L → ∞ and δρ → 0. We considered a system with a large density difference and measured the stationary current through the system: the advantage is that we have to take only one limit, L → ∞.…”