Nonequilibrium Statistical Operator for Systems of Finite Size

TL;DR

This paper introduces a novel approach to nonequilibrium statistical mechanics by incorporating the system's lifetime into the statistical operator, especially for finite-sized systems, replacing traditional methods like invariant parts and coarse-graining.

Contribution

It proposes a new nonequilibrium statistical operator that explicitly includes system lifetime, providing a framework for finite-sized systems and deriving lifetime change expressions during transitions.

Findings

Derived an expression for lifetime change during system transitions.

Suggested a new form of nonequilibrium statistical operator for finite systems.

Replaced traditional averaging methods with lifetime distribution averaging.

Abstract

The lifetime of statistical system is introduced. 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 lifetime change at transitions from quasi-equilibrium system to nonequilibrium one is derived. A sort of the nonequilibrium statistical operator for systems of the finite sizes is suggested.