Differences between Statistical Mechanics and Thermodynamics on the Mesoscopic Scale

TL;DR

This paper investigates the differences between statistical mechanics and thermodynamics in finite disordered systems, showing how spectral correlations influence these differences and how they diminish at high temperatures.

Contribution

It introduces a systematic expansion based on the ratio of level spacing to temperature to analyze spectral correlation effects on thermodynamic behavior.

Findings

Differences are linked to spectral correlations in disordered systems.

Robust differences are suppressed at temperatures much higher than the level spacing.

The expansion method quantifies the transition from quantum to classical thermodynamic behavior.

Abstract

We present a systematic expansion in the ratio between the level spacing and temperature and employ it to evaluate differences between statistical mechanics and thermodynamics in finite disordered systems. These differences are related to spectral correlations in those systems. They are fairly robust and are suppressed at temperatures much higher than the level spacing.