The information-theoretic formulation of statistical mechanics is applied to an ideal gas transporting energy without transporting mass. It is shown that the thermal state variables fracture into distinct populations, thus exhibiting a radical sort of local nonequilibrium. The partition function is found in exact form, for an arbitrarily large temperature gradient. In an approximation, it is shown that these results reduce to the known ones for equilibrium, and near equilibrium. The same approximation allows us specific equations for the temperature, pressure tensor, and the entropy of the system, in a far-from-equilibrium case, in terms of the new thermal variables of the system. The general entropy functional, and its variation, are discussed.

• Received 26 January 1973

DOI:https://doi.org/10.1103/PhysRevA.9.1371