Invariant forms and control dimensional parameters in complexity quantification

Non-equilibrium dynamics is omnipresent in nature and technology can exhibit symmetries order. In idealistic systems this universality well-captured by traditional models of dynamical systems. Realistic processes are often more complex. This work considers two paradigmatic complexities—canonical Kolmogorov turbulence interfacial Rayleigh-Taylor mixing. We employ invariant forms to assess very different properties characteristics these processes. inter-link, for the first time, our knowledge, scaling laws spectral shapes reveal decisive role control dimensional parameters their respective dynamics. find that provide key insights into attributes non-equilibrium dynamics, thus expanding range applicability well-beyond frameworks.