  For classical discrete systems under constant composition, we re-examine how
linear-nonlinear boundary in canonical ensemble, connecting a set of potential
energy surface and that of microscopic configuration in thermodynamic
equilibrium, is characterized by underlying lattice, from tropical geometry. We
here show that by applying suitable tropical limit and multiple coordinate
transform to time evolution of discrete dynamical system, reflecting geometric
aspect of the nonlinearity, we successfully construct tropical diagram
caputuring the universal character of linear/nonlinear region on configuration
space for f = 2 structural degree of freedoms (SDFs). The diagram indicates
that the boundary near disordered state is mainly dominated by constraints to
individual SDF, while quasi linear-nonlinear boundary apart from disordered
state is dominated by local non-separability in SDFs.
