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

TL;DR

This paper explores how different lifetime distributions in non-equilibrium statistical operators affect the system's properties, revealing effects like finite memory and history dependence beyond traditional exponential assumptions.

Contribution

It introduces a family of non-equilibrium statistical operators based on various lifetime distributions, extending the understanding of memory effects in non-equilibrium systems.

Findings

Finite memory effects observed for certain lifetime distributions

Non-equilibrium properties can significantly differ from exponential lifetime assumptions

History and past behavior influence current non-equilibrium dynamics

Abstract

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 behaviour in the past, can have substantial influence on non-equilibrium conduct of the system in a present moment time.