  We explore the idea that non-equilibrium steady states breaking detailed
balance are obtained by deforming trajectories (lines in space-time) that have
been sampled in a reference system with stochastic dynamics obeying detailed
balance, and we ask for the work required to perform this task. These geometric
deformations are not arbitrary but arise through interactions with the
environment, either the manipulation of conserved quantities by an external
agent, or by their exchange with a work reservoir. This view allows to
consistently model the breaking of detailed balance and the accompanying
entropy production without non-conservative forces, and to systematically
extend the notion of thermodynamic ensembles to non-equilibrium steady states.
We illustrate the usefulness of this approach by applying it to suspensions of
active colloidal particles and deriving their thermodynamically consistent
equations of motion.
