There is an important relationship between the net rate \( \Delta r=r_+ - r_-\) and the net thermodynamic force.  Recall the thermodyamic force in the forward direction is related to the likelihood ratio of the forward and backward rates \(e^{\mathcal A/RT} = r_+/r_- = L_+\), and the thermodynamic force in the backward direction is related to the likelihood ratio of the backwards and forward rates \(e^{-\mathcal A/RT} = r_-/r_+ = L_-\)
Then the net rate \(\Delta r\)  can be defined in terms of the net likelihood ratio \(\Delta L = L_+ - L_-\)