Lifetime of nonequilibrium statistical system is considered. It is supposed that the nonequilibrium statistical operator implicitly contains the lifetime. The operations of taking of invariant part, averaging on initial conditions used in works of D. N. Zubarev, temporary coarse‐graining (Kirkwood), choose of the direction of time are replaced by averaging on lifetime distribution. The expression for average lifetime of nonequilibrium system is derived. It is shown, that the nonequilibrium statistical operator in the formulation of D. N. Zubarev describes the lifetime of nonequilibrium systems.

A family of nonequilibrium statistical operators (NSO) is introduced which differ by the system lifetime distribution over which the quasiequilibrium (relevant) distribution is averaged. This changes the form of the source in the Liouville equation, as well as the expressions for the kinetic coefficients, average fluxes, and kinetic equations obtained with use of NSO. The difference from the Zubarev form of NSO is of the order of the reciprocal lifetime of a system. In work [1] the new interpretation of a method of the Nonequilibrium Statistical Operator (NSO) [2,3] is given, in which NSO is treated as averaging of the quasi-equilibrium (or relevant [4,5]) statistical operator on the system past lifetime distribution and NSO rewritten aswhere H is hamiltonian, ln r(t) is the logarithm of the NSO, ln r q (t,0) is the logarithm of the quasi-equilibrium distribution; the first time argument indicates the time dependence of the values of the thermodynamic parameters F m ; the second time argument t 2 in r q (t 1 , t 2 ) denotes the time dependence through the Heizenberg representation for dynamical variables P m from which r q (t,0) can depend [1][2][3]. In [1] the function p q (u) = e exp {-eu} from [2,3] was interpreted as the probability distribution density of the lifetime of a system from the random moment t 0 of its birth till the current moment t; u = t -t 0 . This time period can be called the time period of getting information about system from its past. Instead of the exponential distribution p q (u) in (1) any other sample distribution could be taken. The arbitrary kind of lifetime density distribution p q (u) enables to write down a general view of a source in the dynamic Liouville equation, which thus accepts Boltzmann-Prigogine form and contains dissipative effects [4,5]. It is known [2,3] that the Liouville equation for Zubarev's NSO contains the source J = J zub = = -e [ln r(t) -ln r q (t,0)] which tends to zero after taking the thermodynamic limit and setting e®0, e = -1 , which in the spirit of the paper [1] corresponds to the infinitely large lifetime value of an infinitely large system. For a system with finite size this source is not equal to zero. Besides the Zubarev's form of NSO [2,3], Green-Mori form [6,7] is known, where one assumes the auxiliary weight function [5] to be equalAfter averaging one sets t®¥. This situation at p q (u = t -t 0 ) = w(t, ¢ t = t 0 ) coincides with the uniform lifetime distribution. The source in the Liouville equation takes the form J = ln r q /t. In [2] this form of NSO is compared to the Zubarev's form.One could name many examples of explicit defining of the function p q (u) in (1). Every definition implies some specific form of the source term J in the Liouville equation, some specific form of the modified Liouville opera-

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. A 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. Superstatistics, introduced in works of Beck and Cohen [Physica

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 [Beck C., Cohen E.G.D., Physica A, 2003, 322A, 267] 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).