  An analogy is drawn between version of non-equilibrium thermodynamics a
distribution-based containing an additional thermodynamic first-passage time
parameter, nonequilibrium statistical operator method and extended irreversible
thermodynamics with flows as an additional thermodynamic parameter.
Thermodynamics containing an additional thermodynamic first-passage time
parameter maps to extended irreversible thermodynamics. Various conditions for
the dependence of the distribution parameters of the first-passage time on the
random value of energy, the first thermodynamic parameter, are considered. Time
parameter relaxation time {\tau} of extended irreversible thermodynamics is
replaced by the average first-passage time. Expressions are obtained for the
thermodynamic parameter, the conjugate of the first passage time through the
entropy change, and for the average first passage time through the flows.
