Forced vs Autonomous Systems

This preliminary draft challenges the centuries-old taxonomy in classical mechanics, control theory, and dynamical systems theory that distinguishes between autonomous systems ($\dot{x}=f(x)$) and non-autonomous or forced systems ($\dot{x}=f(x,u(t))$). The paper proves that this dichotomy is an artifact of arbitrary system boundary selection rather than an intrinsic property of physical reality. By incorporating the physical state subspace generating any external forcing function $u(t)$ or driving signal into an expanded state vector ($X=[x,z]^T$), every non-autonomous system collapses identically into a single autonomous transition mapping ($X_{k+1}=f(X_{k})$). Consequently, the concept of an external forcing input is shown to be a computational red herring, and eliminating it unlocks unconstrained parallel execution speeds in discrete state engines.