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A family of non-equilibrium statistical operators (NSO) is introduced whichdiffer by the system lifetime distribution over which the quasi-equilibrium(relevant) distribution is averaged. This changes the form of the source in theLiouville equation, as well as the expressions for the kinetic coefficients,average fluxes, and kinetic equations obtained with use of NSO. It is possibleto choose a class of lifetime distributions for which thermodynamic limitingtransition and to tend to infinity of average lifetime of system is reduced tothe result received at exponential distribution for lifetime, used by Zubarev.However there is also other extensive class of realistic distributions oflifetime of system for which and after to approach to infinity of averagelifetime of system non-equilibrium properties essentially change. For somedistributions the effect of "finite memory" when only the limited interval ofthe past influence on behaviour of system is observed. It is shown, how it ispossible to spend specification the description of effects of memory within thelimits of NSO method, more detailed account of influence on evolution of systemof quickly varying variables through the specified and expanded form of densityof function of distribution of lifetime. The account of character of history ofthe system, features of its behaviour in the past, can have substantialinfluence on non-equilibrium conduct of the system in a present moment time.

Influence of probability density function of the passage time in the  method of non-equilibrium statistical operator on non-equilibrium properties  of the system