  We introduce a model of long-range interacting particles evolving under a
stochastic Monte Carlo dynamics, in which possible increase or decrease in the
values of the dynamical variables is accepted with preassigned probabilities.
For symmetric increments, the system at long times settles to the Gibbs
equilibrium state, while for asymmetric updates, the steady state is out of
equilibrium. For the associated Fokker-Planck dynamics in the thermodynamic
limit, we compute exactly the phase space distribution in the nonequilibrium
steady state, and find that it has a nontrivial form that reduces to the
familiar Gibbsian measure in the equilibrium limit.
