  Non-equilibrium states of a thermodynamic statistical system are investigated
using the thermodynamic parameter of the system lifetime, first-passage time,
the time before degeneration of the system under influence of fluctuations.
Statistical distributions that describe the behavior of energy and lifetime are
used. Entropy and obtained thermodynamic relations are compared with the
results of Extended Irreversible thermodynamics, where as an additional
parameter selected fluxes. Explicit expressions are obtained for average
lifetime and conjugate thermodynamic quantity. It is shown that, when is only
one stationary non-equilibrium state and exponential distribution for the
lifetime, flows can only reduce the average system lifetime. However, there are
possibilities to description of increase the average lifetime of the system. A
description of the growth of the average lifetime for one stationary
non-equilibrium state is possible when choosing distributions for the lifetime,
differing from the limiting exponential distribution.
