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First passage time plays a fundamental role in dynamical characterization ofstochastic processes. Crucially, our current understanding on the problem isalmost entirely relies on the theoretical formulations, which assume theprocesses under consideration are Markovian, despite abundant non-Markoviandynamics found in complex systems. Here we introduce a simple and physicallyappealing analytical framework to calculate the first passage time statisticsof non-Markovian walkers grounded in a fundamental principle of nonequilibriumstatistical physics that connects the fluctuations in stochastic system to themacroscopic law of relaxation. Pinpointing a crucial role of the memory in thefirst passage time statistics, our approach not only allows us to confirm thenon-trivial scaling conjectures for fractional Brownian motion, but alsoprovides a formula of the first passage time distribution in the entire timescale, and establish the quantitative description of the position probabilitydistribution of non-Markovian walkers in the presence of absorbing boundary.

First passage time statistics of non-Markovian random walker: Onsager's regression hypothesis approach