  We study a stochastic many-body system maintained in an non-equilibrium
steady state. Probability distribution functional of the time-integrated
current and density is shown to attain a large-deviation form in the long-time
asymptotics. The corresponding Current-Density Cramer Functional (CDCF) is
explicitly derived for irreversible Langevin dynamics and discrete-space Markov
chains. We also show that the Cramer functionals of other linear functionals of
density and current, like work generated by a force, are related to CDCF in a
way reminiscent of variational relations between different thermodynamic
potentials. The general formalism is illustrated with a model example.
