### Abstract

Recently Lebowitz and Penrose gave a rigorous derivation of the van der Waals-Maxwell theory of the liquid-vapor transition, and showed how the Maxwell equal area-rule could be obtained from a proper statistical mechanical calculation. Their results are quite general - being valid in any number of dimensions and for a broad class of pair potentials - but they were proved only for classical mechanics. In the present work we extend the proof to quantum systems with any statistics - Boltzmann, Bose, or Fermi. One corollary of this extended theorem is a model of a Bose gas with a first-order phase transition.

Original language | English (US) |
---|---|

Pages (from-to) | 1016-1024 |

Number of pages | 9 |

Journal | Journal of Mathematical Physics |

Volume | 7 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 1966 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'Quantum-mechanical extension of the Lebowitz-Penrose theorem on the Van Der Waals theory'. Together they form a unique fingerprint.

## Cite this

Lieb, E. (1966). Quantum-mechanical extension of the Lebowitz-Penrose theorem on the Van Der Waals theory.

*Journal of Mathematical Physics*,*7*(6), 1016-1024. https://doi.org/10.1063/1.1704992