### Abstract

We establish the existence of the infinite volume (thermodynamic) limit for the free energy density of a system of charged particles, e.g., electrons and nuclei. These particles, which are the elementary constituents of macroscopic matter, interact via Coulomb forces. The long range nature of this interaction necessitates the use of new methods for proving the existence of the limit. It is shown that the limit function has all the convexity (stability) properties required by macroscopic thermodynamics. For electrically neutral systems, the limit functions is domain-shape independent, while for systems having a net charge the thermodynamic free energy density is shape dependent in conformity with the well-known formula of classical electrostatics. The analysis is based on the statistical mechanics ensemble formalism of Gibbs and may be either classical or quantum mechanical. The equivalence of the microc anonical, canonical and grand canonical ensembles is demonstrated.

Original language | English (US) |
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Pages (from-to) | 316-398 |

Number of pages | 83 |

Journal | Advances in Mathematics |

Volume | 9 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1972 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

*Advances in Mathematics*,

*9*(3), 316-398. https://doi.org/10.1016/0001-8708(72)90023-0