  We show that the steady-state entropy production rate of a stochastic process
is inversely proportional to the minimal time needed to decide on the direction
of the arrow of time. Here we apply Wald's sequential probability ratio test to
optimally decide on the direction of time's arrow in stationary Markov
processes. Furthermore the steady state entropy production rate can be
estimated using mean first-passage times of suitable physical variables. We
derive a first-passage time fluctuation theorem which implies that the decision
time distributions for correct and wrong decisions are equal. Our results are
illustrated by numerical simulations of two simple examples of nonequilibrium
processes.
