Direct derivation of microcanonical ensemble average from many-particle quantum mechanics

TL;DR

This paper demonstrates how to derive the microcanonical ensemble average of a physical quantity directly from many-particle quantum mechanics using long time averages and the equal probability assumption, within an open system framework.

Contribution

It provides a direct derivation of the microcanonical ensemble average from quantum mechanics without relying on traditional statistical assumptions.

Findings

Derivation of microcanonical average from quantum dynamics

Use of long time averages and equal probability assumption

Framework includes system embedded in an environment

Abstract

Starting from the quantum mechanics for $N$ particles, we show that we can directly derive the microcanonical ensemble average of the physical quantity $A$ by using only the long time average and the equal probability assumption for the equal energy states. The system is considered to be embedded in the outer world and we describe them in terms of the density matrix method.