  The issue of relaxation has been addressed in terms of ergodic theory in the
past. However, the application of that theory to models of physical interest is
problematic, especially when dealing with relaxation to nonequilibrium steady
states. Here, we consider the relaxation of classical, thermostatted particle
systems to equilibrium as well as to nonequilibrium steady states, using
dynamical notions including decay of correlations. We show that the condition
known as {\Omega}T-mixing is necessary and sufficient to prove relaxation of
ensemble averages to steady state values. We then observe that the condition
known as weak T-mixing applied to smooth observables is sufficient for
relaxation to be independent of the initial ensemble. Lastly, weak T-mixing for
integrable functions makes relaxation independent of the ensemble member, apart
from a negligible set of members enabling the result to be applied to
observations from a single physical experiment. The results also allow us to
give a microscopic derivation of Prigogine's principle of minimum entropy
production in the linear response regime. The key to deriving these results
lies in shifting the discussion from characteristics of dynamical systems, such
as those related to metric transitivity, to physical measurements and to the
behaviour of observables. This naturally leads to the notion of physical
ergodicity.
