Entropy production of the contact model

Abstract We propose an expression for the production of entropy for a 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 definite and based on the inequality <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mi>ln</mml:mi> <mml:mo>⁡</mml:mo> <mml:mi>x</mml:mi> <mml:mo>−</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mtext>⩾</mml:mtext> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . 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.