Potentials of homotopy cyclic AI-algebras

For a cyclic $\AI$-algebra, a potential recording the structure constants can be defined. We define an analogous potential for a homotopy cyclic $\AI$-algebra and prove its properties. On the other hand, we find another different potential for a homotopy cyclic $\AI$-algebra, which is related to the algebraic analogue of generalized holonomy map of Abbaspour, Tradler and Zeinalian.