  At equilibrium, a fluid element, within a larger heat bath, receives random
impulses from the bath. Those impulses, which induce stochastic transitions in
the system (the fluid element), respect the principle of detailed balance,
because the bath is also at equilibrium. Under continuous shear, the fluid
element adopts a non-equilibrium steady state. Because the surrounding bath of
fluid under shear is also in a non-equilibrium steady state, the system
receives stochastic impulses with a non-equilibrium distribution. Those
impulses no longer respect detailed balance, but are nevertheless constrained
by rules. The rules in question, which are applicable to a wide sub-class of
driven steady states, were recently derived [R. M. L. Evans, Phys. Rev. Lett.
{\bf 92}, 150601 (2004); J. Phys. A: Math. Gen. {\bf 38}, 293 (2005)] using
information-theoretic arguments. In the present paper, we provide a more
fundamental derivation, based on the uncontroversial, non-Bayesian
interpretation of probabilities as simple ratios of countable quantities. We
apply the results to some simple models of interacting particles, to
investigate the nature of forces that are mediated by a non-equilibrium
noise-source such as a fluid under shear.
