  The nonequilibrium stationary state of an irreversible spherical model is
investigated on hypercubic lattices. The model is defined by Langevin equations
similar to the reversible case, but with asymmetric transition rates. In spite
of being irreversible, we have succeeded in finding an explicit form for the
stationary probability distribution, which turns out to be of the
Boltzmann-Gibbs type. This enables one to evaluate the exact form of the
entropy production rate at the stationary state, which is non-zero if the
dynamical rules of the transition rates are asymmetric.
