  In this paper we investigate the applicability of non-equilibrium statistical
mechanics to non-equilibrium damage phenomena. As an example, a fiber-bundle
model with thermal noise and a fiber-bundle model with decay of fibers are
considered. Initially we develop an analogy of the Gibbs formalism for
nonequilibrium states. Later we switch from the approach of non-equilibrium
states to the approach of non-equilibrium paths. Fluctuating behavior in the
system is described in terms of effective temperature parameters. An equation
of state and an analog of an energy-balance equation are obtained. Also the
formalism of the free energy potential is developed. For fluctuations of paths
in the system the statistical distribution is found to be Gaussian.
