The Thermodynamic Limit of Quantum Coulomb Systems. Part I. General Theory

TL;DR

This paper establishes general conditions under which the energy of quantum Coulomb systems has a well-defined thermodynamic limit, providing a foundation for analyzing large-scale quantum systems.

Contribution

It introduces sufficient conditions for the existence of thermodynamic limits of energy functions in quantum Coulomb systems, with clear physical interpretations.

Findings

Conditions are provided for the existence of thermodynamic limits.

The framework applies to a broad class of quantum Coulomb systems.

Next work will verify these conditions for specific systems.

Abstract

This article is the first in a series dealing with the thermodynamic properties of quantum Coulomb systems. In this first part, we consider a general real-valued function $E$ defined on all bounded open sets of $\R^3$. Our aim is to give sufficient conditions such that $E$ has a thermodynamic limit. This means that the limit $E(\Omega_n)|\Omega_n|^{-1}$ exists for all `regular enough' sequence $\Omega_n$ with growing volume, $|\Omega_n|\to\ii$, and is independent of the considered sequence. The sufficient conditions presented in our work all have a clear physical interpretation. In the next paper, we show that the free energies of many different quantum Coulomb systems satisfy these assumptions, hence have a thermodynamic limit.