  To describe the nonequilibrium states of a system we introduce a new
thermodynamic parameter - the lifetime (the first passage time) of a system.
The statistical distributions that can be obtained out of the mesoscopic
description characterizing the behaviour of a system by specifying the
stochastic processes are written. Superstatistics, introduced in [1] as
fluctuating quantities of intensive thermodynamical parameters, are obtained
from statistical distribution with lifetime (random time to system degeneracy)
as thermodynamical parameter (and also generalization of superstatistics).
Necessary for this realization condition with expression for average lifetime
of stationary statistical system obtained from stochastical storage model [32]
is consisting. The obtained distribution passes in Gibbs distribution depending
on a measure of deviation from equilibrium related to fluxes and dissipativity
in the system.
