  We consider nonclassical entropy solutions to scalar conservation laws with
concave-convex flux functions, whose set of left- and right-hand admissible
states across undercompressive shocks is selected by a kinetic function \phi.
We introduce a new definition for the (generalized) strength of classical and
nonclassical shocks, allowing us to propose a generalized notion of total
variation functional. Relying only upon the natural assumption that the
composite function \phi o \phi is uniformly contracting, we prove that the
generalized total variation of front-tracking approximations is non-increasing
in time, and we conclude with the existence of nonclassical solutions to the
initial-value problem. We also propose two definitions of generalized
interaction potentials which are adapted to handle nonclassical entropy
solutions and we investigate their monotonicity properties. In particular, we
exhibit an interaction functional which is globally non-increasing along a
splitting-merging interaction pattern.
