Constructing non-equilibrium statistical ensemble formalism based on Subdynamics

TL;DR

This paper develops a non-equilibrium statistical ensemble formalism using subdynamics, employing similarity transformations to connect with Gibbsian ensembles, and explores applications in quantum systems like Cayley trees and spin networks.

Contribution

It introduces a novel non-equilibrium ensemble formalism based on subdynamics and similarity transformations, extending quantum canonical ensemble analysis.

Findings

Derived a projected density distribution capturing irreversible evolution

Generalized reduced density distribution for quantum canonical ensembles

Applied formalism to Cayley tree and spin network models

Abstract

In this work, we present a general non-equilibrium ensemble formalism based on the subdynamic equation (SKE). The constructing procedure is to use a similarity transformation between Gibbsian ensemble formalism and the non-equilibrium ensemble formalism. The obtained density distribution is a projected one that can represent essence part of (irreversible) evolution of the density distribution, by which a generalized reduced density distribution for the quantum canonical ensembles is studied and applications in Cayley tree and spin network are discussed.