  We propose an expression for the production of entropy for system described
by a stochastic dynamics which is appropriate for the case where the reverse
transition rate vanishes but the forward transition is nonzero. The expression
is positive defined and based on the inequality $x\ln x-(x-1)\ge0$. The
corresponding entropy flux is linear in the probability distribution allowing
its calculation as an average. The expression is applied to the one-dimensional
contact process at the stationary state. We found that the rate of entropy
production per site is finite with a singularity at the critical point with
diverging slope.
