Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. Superstatistics, introduced in works of Beck and Cohen [Physica A \textbf{322}, (2003), 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment.Comment: 18 page

Stability criteria and fluctuations around nonequilibrium states

A stochastic formulation of the stability of, nonequilibrium states is discussed. An entropy balance equation, including the effect of both the macroscopic evolution and of the fluctuations is derived. In the linear region of thermodynamics Prigogine's minimum entropy production, theorem is extended to include the effect of fluctuations. The latter are shown to reïnforce the return of the system to its steady state distribution. © 1984 Springer-Verlag.SCOPUS: ar.jinfo:eu-repo/semantics/publishe