  In this paper we will attempt to answer the following question: what are the
natural quantum subsystems which emerge out of a system's dynamical laws? To
answer this question we first define generalized tensor product structures
(gTPS) in terms of observables, as dual pairs of an operator subalgebra $\cal
A$ and its commutant. Second, we propose an operational criterion of minimal
information scrambling at short time scales to dynamically select gTPS. In this
way the emergent subsystems are those which maintain the longest informational
identity. This strategy is made quantitative by defining a Gaussian scrambling
rate in terms of the short-time expansion of an algebraic version of the Out of
Time Order Correlation (OTOC) function i.e., the $\cal A$-OTOC. The Gaussian
scrambling rate is computed analytically for physically important cases of
general division into subsystems, and is shown to have an intuitive and
compelling physical interpretation in terms of minimizing the interaction
strength between subsystems.
