Properties of Symmetry of Space and Time, Hamilton's Principle and the Invariants

This research investigates the fundamental role of symmetry properties in space and time in justifying the use of the principle of least action (PLA) to describe the creation and evolution of nanomaterials. By examining the kinetics of structural transformations in metals, we demonstrate that the PLA is a universal principle applicable to diverse physicochemical and biological processes. We explore the principle's ability to establish invariants at various structural-scale levels of metal deformation, including nano-, submicro-, micro-, meso-, and macroscale levels. Our findings highlight the significance of symmetry properties in understanding and predicting the behavior of nanomaterials.