Entropy production of the contact model

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 xln x-(x-1)≥0. 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.