Entropy alternatives for equilibrium and out of equilibrium systems

TL;DR

This paper introduces new entropy-related measures, non-repeatability and mutability, to analyze complex systems' dynamics, demonstrating their sensitivity to data ordering and their ability to reveal critical behaviors in physical and seismic systems.

Contribution

The paper proposes non-repeatability and mutability as novel entropy measures that are sensitive to temporal order, providing new insights into system dynamics beyond traditional entropy.

Findings

Non-repeatability and mutability are sensitive to data ordering.

Sorted mutability reveals critical behavior in systems.

Proposed measures differ from Shannon entropy in capturing dynamics.

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.