  For classical discrete system under constant composition, typically reffered
to as substitutional alloys, canonical average acts as nonlinear map F from a
set of potential energy surface U to that of microscopic configuration in
thermodynamic equilibrium, Q, which is called canonical nonlinearity (CN). On
statistical manifold, at any given configuration, F can be divided into the sum
of local and non-local contribution in terms of Kullback-Leibler (KL)
divergence, where the former has strong positive correlation with time
evolution of the nonlinearity (NOL) on configuration space (called
anharmonicity in structural degree of freedoms (ASDF), while the latter,
corresponding to entanglement in SDFs, does exhibit clear correlation with the
ASDF. On the other hand, our recent work bridge the different concepts of NOL
on configuration space and statistical manifold through stochastic
thermodynamics. While the work successfully provides clear relationships
between the changes in total NOL through system transition and heat transfer,
thermodynamic interpretation of how the entanglment in SDFs contributes to
thermodynamic functions, is totally unclear due mainly to its non-trivial,
non-local character. The present study tackle this problem, deriving upper
bound for the entanglement for any given transition in terms of the mutual
information, heat transfer and free energy. The present thermodynamic
interpretaion will provide quantitative description of how the entanglement in
SDFs is dominated by configuration of ground-state structures on configuration
space.
