The Thermodynamic Limit of Quantum Coulomb Systems. Part I. General   Theory
  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. 
Christian Hainzl, Mathieu Lewin and Jan Philip Solovej