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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.