  We introduce and study potentials, mutations and Jacobian algebras in the
framework of tensor algebras associated with symmetrizable dualizing pairs of
bimodules on a symmetric algebra over any commutative ground ring. The graded
context is also considered by starting from graded bimodules, and the classical
non simply-laced context of modulated quivers with potentials is a particular
case. The study of potentials in this framework is related to symmetrically
separable algebras, and we have two kinds of potentials: the symmetric and the
non symmetric ones. When the Casimir ideal of the symmetric algebra coincides
with its center, all potentials appear as symmetric potentials and their
manipulation mimics the simply laced study of quivers with potentials. This
useful information suggests that, for applications to cluster algebras theory
and related fields, one may restrict a further study of modulated quivers with
potentials to the setting where the ground symmetric algebra is separable over
a field. Associated with this work is a generalized construction of Ginzburg
dg-algebras and cluster categories associated with graded modulated quivers
with potentials.
