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

Comparison of extended irreversible thermodynamics and nonequilibrium  statistical operator method with thermodynamics based on a distribution  containing the first-passage time