  With nontrivial entropy production, first passage process is one of the most
common nonequilibrium process in stochastic thermodynamics. Using one
dimensional birth and death precess as a model framework, approximated
expressions of mean first passage time (FPT), mean total number of jumps (TNJ),
and their coefficients of variation (CV), are obtained for the case far from
equilibrium. Consequently, uncertainty relations for FPT and TNJ are presented.
Generally, mean FPT decreases exponentially with entropy production, while mean
TNJ decreases exponentially first and then tends to a starting site dependent
limit. For forward biased process, the CV of TNJ decreases exponentially with
entropy production, while that of FPT decreases exponentially first and then
tends to a starting site dependent limit. For backward biased process, both CVs
of FPT and TNJ tend to one for large absolute values of entropy production.
Related properties about the case of equilibrium are also addressed briefly for
comparison.
