Before revision:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.
After revision:  Moreover, we provide a dual characterization of the dynamic property , i.e. we show that \mathcal{E}_t} (\cdot)}\colon } \to\mathbb{R which leaves the constants invariant, the tower property \mathcal{E}(\cdot)} =\mathcal{E} _t\circ\mathcal{E_{t+1} if and only if the convex conjugate of \mathcal{E}_t has an additive form.