  One of the key features of non-equilibrium steady states (NESS) is the
presence of nontrivial probability currents. We propose a general
classification of NESS in which these currents play a central distinguishing
role. As a corollary, we specify the transformations of the dynamic transition
rates which leave a given NESS invariant. The formalism is most transparent
within a continuous time master equation framework since it allows for a
general graph-theoretical representation of the NESS. We discuss the
consequences of these transformations for entropy production, present several
simple examples, and explore some generalizations, to discrete time and
continuous variables.
