Algorithmic Approaches for Assessing Multiscale Irreversibility in Time Series: Review and Comparison

Many physical and biological phenomena are characterized by time asymmetry, and are referred to as irreversible. Time-reversal symmetry breaking is in fact the hallmark of systems operating away from equilibrium and reflects the power dissipated by driving the system away from it. Time asymmetry may manifest in a wide range of time scales; quantifying irreversibility in such systems thus requires methods capable of detecting time asymmetry in a multiscale fashion. In this contribution we review the main algorithmic solutions that have been proposed to detect time irreversibility, and evaluate their performance and limitations when used in a multiscale context using several well-known synthetic dynamical systems. While a few of them have a general applicability, most tests yield conflicting results on the same data, stressing that a "one size fits all" solution is still to be achieved. We conclude presenting some guidelines for the interested practitioner, as well as general considerations on the meaning of multiscale time irreversibility.