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

TL;DR

This paper introduces a family of non-equilibrium statistical operators based on system lifetime distributions, linking superstatistics to lifetime fluctuations and emphasizing the importance of system evolution history in non-equilibrium behavior.

Contribution

It proposes a novel approach to non-equilibrium statistical mechanics by integrating lifetime distributions and superstatistics, considering the system's evolution stages.

Findings

Lifetime distributions vary across different system evolution stages.

Superstatistics can be derived from lifetime fluctuation distributions.

Past system evolution significantly influences current non-equilibrium states.

Abstract

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.