Abstract
The statistical mechanics of steady flows, heat and shear, are presented in detail. For heat flow, the canonical non-equilibrium system, the phase space probability density is given explicitly. An equipartition theorem is derived. The stochastic dissipative equations of motion for phase space are also given. A fluctuation dissipation theorem is derived from the second entropy. Several Green-Kubo expressions for the thermal conductivity are derived, and their relation with the odd projection of the dynamic part of the reservoir entropy is discussed. The analysis is repeated for shear flow, for which the non-equilibrium probability density in phase space is given, as well as a Green-Kubo expression for the shear viscosity.
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