Memory Index of First-Passage Time: A Simple Measure of Non-Markovian Character

The theory is developed for the second moment of the first-passage-time variable of statistical flows with memory (non-Markovian dynamics) and applied to a model of free non-Markovian Brownian motion. More importantly, a novel quantity, called memory index $\sigma$, is introduced, giving a quantitative characterization of the influence on non-Markovian behavior. Thus, a theoretical or experimental evaluation of $\sigma$ allows one to assess the quality of widely used approximative (Markovian) Fokker-Planck-type descriptions of the dynamics.