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The composite systems can be non-uniquely decomposed into parts (subsystems). Not all decompositions (structures) of a composite system are equally physically relevant. In this paper we answer on theoretical ground why it may be so. We consider a pair of mutually un-coupled modes in the phase space representation that are subjected to the independent quantum amplitude damping channels. By investigating asymptotic dynamics of the degrees of freedom, we find that the environment is responsible for the structures non-equivalence. Only one structure is distinguished by both locality of the environmental influence on its subsystems and a classical-like description. [ABSTRACT FROM AUTHOR]