  We derive generic thermodynamic bounds on the moments of first-passage times
of dissipative currents in nonequilibrium stationary states. These bounds hold
generically for nonequilibrium stationary states in the limit where the
threshold values of the current that define the first-passage time are large
enough. The derived first-passage time bounds describe a tradeoff between
dissipation, speed, reliability, and a margin of error and therefore represent
a first-passage time analogue of thermodynamic uncertainty relations. For
systems near equilibrium the bounds imply that mean first-passage times of
dissipative currents are lower bounded by the Van't Hoff-Arrhenius law. In
addition, we show that the first-passage time bounds are equalities if the
current is the entropy production, a remarkable property that follows from the
fact that the exponentiated negative entropy production is a martingale.
Because of this salient property, the first-passage time bounds allow for the
exact inference of the entropy production rate from the measurements of the
trajectories of a stochastic process without knowing the affinities or
thermodynamic forces of the process.
