First-Passage Time: A Conception Leading to Superstatistics. I.   Superstatistics with Discrete Distributions
  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. 
V. V. Ryazanov