Invariant energy symmetries independent of action principle: Unifying equilibrium and non-equilibrium dynamics

Abstract

Understanding energy dynamics across physical systems requires principles that extend beyond equilibrium and Lagrangian formulations. However, a general symmetry-based description of energy behavior that remains valid without invoking an action principle is still lacking. Here we show that energy dynamics can be formulated in terms of invariant symmetry structures acting directly on energy composition and exchange. By analyzing these structure-preserving transformations, we identify stable energy symmetries whose restriction or breaking gives rise to familiar laws such as classical mechanics and thermodynamics. The framework is developed independently of any specific thermodynamic theory; dynamic/non-dynamic decompositions, including GEB-type formulations and structurally motivated thermodynamic viewpoints, are used only as representative realizations. This approach provides a unified perspective on equilibrium, non-equilibrium, and complex systems, and is supported by both conceptual arguments and numerical tests in driven dissipative scenarios.