  Thermodynamic quantities of the hard-sphere system in the steady state with a
small heat flux are calculated within the continuous media approach. Analytical
expressions for pressure, internal energy, and entropy are found in the
approximation of the fourth order in temperature gradients. It is shown that
the gradient contributions to the internal energy depend on the volume, while
the entropy satisfies the second law of thermodynamics for nonequilibrium
processes. The calculations are performed for dimensions 3D, 2D, and 1D.

Statistical Mechanics