Effects of Sample Specific Variations and Fluctuations of Thermal Occupancy on Fluctuations of Thermodynamic Quantities

TL;DR

This paper investigates how sample-specific variations and thermal occupancy fluctuations jointly influence thermodynamic quantity fluctuations, focusing on particle number and specific heat in a 2D electron gas under different dynamical regimes.

Contribution

It introduces a combined analysis of mesoscopic and thermal occupancy fluctuations affecting thermodynamic quantities in non-interacting electron systems.

Findings

Mesoscopic fluctuations significantly impact thermodynamic quantities.

Differences observed between integrable and chaotic systems.

Quantitative evaluation of particle number and specific heat fluctuations.

Abstract

Standard results for the fluctuations of thermodynamic quantities are derived under the assumption of sampling identical systems that are in different, not fully equilibrated states. These results apply to fluctuations with time in a particular macroscopic body and can be traced to the fluctuations of thermal occupancy. When many identically prepared - but not identical - systems are studied, mesoscopic fluctuations due to variations from sample to sample contribute to the fluctuations of thermodynamic quantities. We study the combined effect of mesoscopic fluctuations and fluctuations of thermal occupancy. In particular, we evaluate the total particle number and specific heat fluctuations in a two-dimensional, non-interacting electron gas in classically integrable and chaotic circumstances.