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A variational principle for thermostated nonequilibrium steady states recently proposed by Evans and Baranyai [Phys. Rev. Lett. 67, 2597]is analyzed by means of a model kinetic equation for dilute gases. It is shown that the principle does not apply exactly, although deviations from it are small, especially when the gradients are not very large, PACS numbers: 47.50.+d, 05.20.Dd, 05.60.+w, 51.10. +y I"ar from equilibrium systems have turned out very difficult to study, and there is not a generaldoi:10.1103/physrevlett.70.2730 pmid:10053638 fatcat:ieu6c6ntprdf7bdlchgsvxvlcq