Family of non-equilibrium statistical operators and influence of the   past on the present
  A family of non-equilibrium statistical operators (NSO) is introduced which differ by the system lifetime distribution over which the quasi-equilibrium (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. It is possible to choose a class of lifetime distributions for which thermodynamic limiting transition and to tend to infinity of average lifetime of system is reduced to the result received at exponential distribution for lifetime, used by Zubarev. However there is also other extensive class of realistic distributions of lifetime of system for which and after to approach to infinity of average lifetime of system non-equilibrium properties essentially change. For some distributions the effect of "finite memory" when only the limited interval of the past influence on behaviour of system is observed. It is shown, how it is possible to spend specification the description of effects of memory within the limits of NSO method, more detailed account of influence on evolution of system of quickly varying variables through the specified and expanded form of density of function of distribution of lifetime. The account of character of history of the system, features of its conduct in the past, can have substantial influence on non-equilibrium conduct of the system in a present moment time. 
V.V. Ryazanov