On the generalized bulk viscosity behavior

We have calculated generalized longitudinal, eta (L)(k), shear, eta (S)(k), and bulk, eta (B)(k) viscosity of argon at two thermodynamic states by molecular-dynamics simulation. Bulk viscosity has been evaluated with two independent methods that give results in good agreement. We find that bulk viscosity stays positive at all wave numbers k, and show that negative values of eta (B)(k) are due to a straightforward (and incorrect) extension to finite k's of the relation eta (B)(k) = eta (L)(k)-4 eta (S)(k)/3, only valid at vanishing k's