Thermodynamic pressure in nonequilibrium gases

We analyze the nonequilibrium thermodynamic pressure which is obtained by differentiation of a generalized nonequilibrium entropy. It is proposed that this nonequilibrium thermodynamic pressure, {π}, is related to the pressure tensor P in the presence of a homogeneous heat flux q{→} through P={π}U+{α}q{→} q{→}, with {α} given by the condition trP=3p, p being the local-equilibrium pressure. A simple situation illustrating the physical difference between {π} and p is presented. The nonequilibrium entropy, pressure, and pressure tensor are also analyzed from a microscopic point of view in several systems.