  In the article \cite{BM1.22}, the minimum volume entropy is introduced for
each group of finite presentation and there we study some of its general
properties. Another concept of minimum volume entropy for geometrically finite
groups has recently been defined in \cite{BC21}. In this paper, we present a
comparative analysis of these two notions which coincide if the geometric
dimension is equal to $1$; they are quite close in dimension $2$ but they
differ radically in the other cases. Finally, we introduce a class of groups
called soft groups, for which we calculate the minimum volume entropy defined
in \cite{BM1.22}. This class contains several known groups, for example,
generalized Baumslag-Solitare groups as well $SL(2,\mathbb{Z})$. The volume
entropy defined in \cite{BC21}, in general, does not apply to soft groups.

Group Theory;Algebraic Geometry;Geometric Topology;Metric Geometry