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