  Generalizations of the microcanonical and canonical ensembles for paths of
Markov processes have been proposed recently to describe the statistical
properties of nonequilibrium systems driven in steady states. Here we propose a
theory of these ensembles that unifies and generalizes earlier results, and
show how it is fundamentally related to the large deviation properties of
nonequilibrium systems. Using this theory, we provide conditions for the
equivalence of nonequilibrium ensembles, generalizing those found for
equilibrium systems, construct driven physical processes that generate these
ensembles, and re-derive in a simple way known and new product rules for their
transition rates. A nonequilibrium diffusion model is used to illustrate these
results.
