15-06U

For a low-density gas, the free energy of the weakly nonequilibrium heat-conduction steady state is calculated. Its nonequilibrium part is obtained in the form of a development in gradients of the local temperature up to the 4-th order. The results are analyzed from the viewpoint of the method of thermodynamic potentials of equilibrium thermodynamics. It is shown that the free energy is not consistent with the entropy found out previously, and has not properties of a thermodynamic potential. Reasons and possible ways to overcome this contradiction are discussed.