Non-Equilibrium Force Formalism and Its Wave- Like Structure

We present a detailed mathematical formulation of a non-equilibrium force defined for open, multi-body systems and apply it to gravitational configurations such as the Earth–Moon system. The force vanishes identically at equilibrium and therefore does not describe binding strength or stability. Instead, it determines spatial configuration through equilibrium separation alone. By carefully expanding the governing equations, we show that temporal variations of system complexity induce a wave-like structure in which complexity acts as an effective medium. Within this framework, gravitational and electromagnetic waves are interpreted as unified modes of non-equilibrium information propagation rather than oscillations of force itself.