Entropy alternatives for equilibrium and out of equilibrium systems

Abstract: We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a dynamical entropy measure. To present the scope and advantages of these quantities, we analyze two distinct systems: (a) Monte Carlo simulations of magnetic moments on a square lattice and (b) seismic time series from the United States Geological Survey catalog. Both systems are well-established in the literature, serving as robust benchmarks. Shannon entropy is employed as a reference point to assess the similarities and differences with the proposed measures. A key distinction lies in the sensitivity of non-repeatability and mutability to the temporal ordering of data, which contrasts with traditional entropy definitions. Moreover, \textit{sorted mutability} -- the mutability computed from a reordered data version -- reveals additional insights into the critical behavior of the systems under study.