  We derive universal thermodynamic inequalities that bound from below the
moments of first-passage times of stochastic currents in nonequilibrium
stationary states of Markov jump processes in the limit where the thresholds
that define the first-passage problem are large. These inequalities describe a
tradeoff between speed, uncertainty, and dissipation in nonequilibrium
processes, which are quantified, respectively, with the moments of the
first-passage times of stochastic currents, the splitting probability, and the
mean entropy production rate. Near equilibrium, the inequalities imply that
mean first-passage times are lower bounded by the Van't Hoff-Arrhenius law,
whereas far from thermal equilibrium the bounds describe a universal speed
limit for rate processes. When the current is the stochastic entropy
production, then the bounds are equalities, a remarkable property that follows
from the fact that the exponentiated negative entropy production is a
martingale.
