On the density matrix of nonequilibrium steady-state statistical   mechanics
  This paper derives a density matrix of the steady-state statistical mechanics compatible with the steady-state thermodynamics proposed by Oono and Paniconi [Prog. Theor. Phys. Suppl. {\bf 130}, 29 (1998)]. To this end, we adopt three plausible basic assumptions for uniform steady states: (i) equivalence between any two subsystems of the total, (ii) statistical independence between any two subsystems, and (iii) additivity of energy. With a suitable definition of energy, it is then shown that uniform steady states driven by mechanical forces may be described by the Gibbs distribution. 
Takafumi Kita