Let G be a free-by-cyclic group or a 2-dimensional right-angled Artin group. We provide an algebraic and a geometric characterization for when each aspherical simplicial complex with fundamental group isomorphic to G has minimal volume entropy equal to 0. In the nonvanishing case, we provide a positive lower bound to the minimal volume entropy of an aspherical simplicial complex of minimal dimension for these two classes of groups. Our results rely upon a criterion for the vanishing of the minimal volume entropy for 2-dimensional groups with uniform uniform exponential growth. This criterion is shown by analyzing the fiber \(\pi _1\)-growth collapse and non-collapsing assumptions of Babenko–Sabourau (Minimal volume entropy and fiber growth, arXiv:2102.04551, 2020).

令G为自由循环群或二维直角 Artin 群。我们提供了一个代数和几何表征，当每个具有同构于G 的基本群的非球面单纯复形具有等于 0 的最小体积熵时。在非零的情况下，我们提供了一个非球面单纯复形的最小体积熵的正下界这两类组的最小维度。我们的结果依赖于具有均匀均匀指数增长的二维组的最小体积熵消失的标准。该准则通过分析纤维\(\pi _1\)- Babenko-Sabourau 的增长崩溃和非崩溃假设（最小体积熵和纤维增长，arXiv:2102.04551, 2020）。