Non-Asymptotic Thermodynamic Ensembles

TL;DR

This paper develops a non-asymptotic framework for thermodynamic ensembles applicable to small systems, using Boltzmann's principle to define probabilities and thermodynamic relations beyond the thermodynamic limit, relevant to nanoscience and quantum tech.

Contribution

It introduces a non-asymptotic approach to thermodynamic ensembles for small systems, extending classical thermodynamics to finite particle numbers in classical and quantum contexts.

Findings

Defines probability distributions for small microcanonical systems.

Constructs thermodynamic relationships without the thermodynamic limit.

Applicable to nanoscience and quantum technology.

Abstract

Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The inferred probability distributions provide the means to define intensive variables and construct thermodynamic relationships for small microcanonical systems, which do not satisfy the thermodynamic limit. This is of critical importance to nanoscience and quantum technology.