  For substitutional alloys, typically refered to as classical discrete systems
under constant composition, we theoretically examine the role of hidden
structure information on evolution of nonlinearity (i.e., correspondence
between a set of potential energy surface and that of many-body interaction) in
canonical ensemble, in terms of the stochastic thermodynamics. When
thermodynamic properties for a given paritial system is controlled by those for
e.g., bulk as a hidden structure information, we derive that change in
nonlinearity on statistical manifold through any transition is identical to the
sum of negative bath entropy change, fluctuation of system entropy change and
fluctuation of stochastic mutual information change between the system
interested and hidden system: We successfully establish basic formulation of
how geometric aspect of nonlinearity evolves under feedback from hidden system
information, which especially provides deeper insight into the nonlinearity for
surface and interface alloys controlled under bulk thermodynamics.
