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Current is a characteristic feature of nonequilibrium systems. In stochasticsystems, these currents exhibit fluctuations constrained by the rate ofdissipation in accordance with the recently discovered thermodynamicuncertainty relation. Here, we derive a conjugate uncertainty relationship forthe first passage time to accumulate a fixed net current. More generally, weuse the tools of large-deviation theory to simply connect current fluctuationsand first passage time fluctuations in the limit of long times and largecurrents. With this connection, previously discovered symmetries and bounds onthe large-deviation function for currents are readily transferred to firstpassage times.

Fundamental Bounds on First Passage Time Fluctuations for Currents