  Recently a novel concise representation of the probability distribution of
heat conducting nonequilibrium steady states was derived. The representation is
valid to the second order in the ``degree of nonequilibrium'', and has a very
suggestive form where the effective Hamiltonian is determined by the excess
entropy production. Here we extend the representation to a wide class of
nonequilibrium steady states realized in classical mechanical systems where
baths (reservoirs) are also defined in terms of deterministic mechanics. The
present extension covers such nonequilibrium steady states with a heat
conduction, with particle flow (maintained either by external field or by
particle reservoirs), and under an oscillating external field. We also simplify
the derivation and discuss the corresponding representation to the full order.
