  For classical discrete system under constant composition typically referred
to substitutional alloys, we examine local nonlinearity in canonical average
phi . We have respectively investigated the local and global behavior of
nonlinearity through previously-introduced vector field A and through tropical
limit of the vector field. While these studies indicated the importance of
constraints to structural degree of freedoms (SDFs) for global nonlinearity, it
has been still unclear how the constraints to SDF affects local nonlinearity.
Based on statistical manifold, we make intuitive bridge between the SDF-based
information and local nonlinearity, decomposing the local nonlinearity into two
(for binary alloys with pair correlations) or three (for otherwise)
contributions in terms of the Kullback-Leibler divergence, where this
decomposition is independent of temperature and many-body interaction, and is
defined on individual configuration. We also find that we can provide
A-dependent as well as A-independent decomposition of the local nonlinearity,
where non-separability in SDFs and its nonadditive character is independent of
A, which indicates that information about evolution of the vector field should
be required to address the non-separability and nonadditivity. The present work
enables to quantify how configuration-dependent constraints to SDF affect local
nonlinearity in canonical average for multicomponent alloys.
