Comment on analysis of transport properties determined by Langevin dynamics using Green–Kubo formulae

• Molecular dynamics simulations based on Langevin models are considered.
• A correction is presented for the Green–Kubo Prandtl number derived by Zhang et al.
• The relationship between Green–Kubo and Boltzmann equation Prandtl numbers is analytically explained.

The development of Langevin models for molecular dynamics represents a promising approach to deal with the cost issue of Boltzmann equation solutions. A recent paper of Zhang et al. suggested to study the Prandtl number variability of such molecular Langevin models under equilibrium conditions. This paper comments on several questions related to the approach of Zhang et al. First, a correction is presented for the Green–Kubo minimum Prandtl number derived by Zhang et al. Second, the relationship between the Green–Kubo Prandtl number and a Prandtl number defined in the Boltzmann equation sense is analytically explained. Third, based on this relationship it is shown that the consideration of a Prandtl number defined in the Boltzmann equation sense represents a more appropriate approach to address the question considered.