Theory Of Imbalance Of Energy v2.0. Synthesis PAPER 1- A Least-Action Formulation of Interaction with Explicit Imbalance Degrees of Freedom

This paper introduces a least-action formulation developed within the Theory of Imbalance of
Energy (TIE), in which dynamical degrees of freedom associated with interaction are represented
explicitly rather than being absorbed into instantaneous force laws. The variational principle
itself is unchanged. Equilibrium is treated as a constraint on admissible configurations, while
imbalance is introduced as a dynamical contribution to the action that stores and redistributes
energy over finite timescales.
The resulting structure yields coupled equations of motion for configuration variables and im
balance variables. In the limit where imbalance redistributes rapidly compared to configuration
evolution, the formalism reduces to standard classical mechanics with instantaneous interaction.
No applications are presented in this paper, and no empirical claims are made. The purpose
of this work is to establish a mathematically consistent, deterministic, and causally well-posed
formal foundation for subsequent analyses within the TIE framework.