In Ref. [1], Garrido et al. studied the heat conduction of a simple one-dimensional gas model consisting of hardpoint particles with alternating masses interacting via elastic collisions. They observed a t ÿ1ÿ > 0 decay law for the current self-correlation function and made a conclusion that the Fourier law holds well, although their direct calculation of JN=T 2 ÿ T 1 did not show a definite evidence of the finite thermal conductivity. The convergence of the thermal conductivity was explained

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... the result of a cooperative behavior in which light particles absorb more energy than the heavier ones. This result means that alternating masses can lead to normal heat conduction and is in contrast with the analytic result [2] that the one-dimensional system with momentum conservation and nonzero pressure have infinite thermal conductivity. Thus, it is necessary to check this result carefully again. In our simulation, the parameters of the model are the same as in Ref. [1]. The direct calculation for the thermal conductivity shows a divergent result agreeing with Garrido et al. qualitatively. But we do not think that is a size effect as authors of Ref. [1] did, since we cannot see any tendency of convergence even at N 8000: The divergence of is fitted by N very well with 0:33, which is very close to that of the FPU model [3] and the diatomic Toda model [4]. The main divergence between their calculation and ours comes from the result of the total current correlation function. The authors declared a t ÿ1ÿ > 0 decay law, while we obtain a t ÿ one with 0:67 (see Fig. 1(a) ) which confirms the divergence of heat conductivity according to the Green-Kubo formula. However, the following additional numerical details are helpful to this question. The authors [1] found that the decay rate of the local current self-correlation function hj0jti and the total current correlation function are close to each other. We have also calculated hj0jti and obtained the same result. The question is that, in our case, the total one and the local one are different qualitatively. We would like to point out that these two quantities should not be the same theoretically. For example, in the case of the gas model with equal masses, the decay law of the correlation function of the local heat current is t ÿ3 [1] while the total current correlation function is a constant since Jt keeps unchanged [Jt P j i t c]. This is why the equal mass model has an abnormal heat conduction. The above results of correlation functions are calculated in the common way as in Ref. [5]. If one proceeds his calculation with initial conditions differing from the Maxwell distribution, one may have a chance to get a similar result as in Ref. [1]. For example, we do find a decay law t ÿ1ÿ > 0 for hJ0Jti with a uniform initial velocities distribution of particles. Finally, a recent paper [6] shows us another argument related to the diatomic gas model. In Ref. [1], the authors declared that the light particles are offered more energy than the heavier ones, while in Ref. [6] the authors obtained an opposite conclusion according to their theoretical analysis. Our calculations show that the latter is correct. The light particles are offered more energy at the beginning, but the situation is changed when the evolution time is long enough [see Fig. 1(b) ]. In conclusion, our numerical calculations do not support the normal heat conduction for the diatomic gas model.