### Abstract

The difficulties inherent in the construction of two-dimensional pressure ensembles are discussed, and are tackled by defining an energy cost depending on the convex hull of the set of particles. An energy proportional to the area of the convex hull is not able to prevent evaporation of the system, whereas an energy proportional to the area of the circumcircle of the convex hull ensures a thermodynamic behavior. In the latter model, which turns out to be exactly solvable, various characterizations are given of the geometry of a typical state. © 1989 Plenum Publishing Corporation.

Original language | English |
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Pages (from-to) | 1059-1068 |

Number of pages | 10 |

Journal | Journal of Statistical Physics |

Volume | 57 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - Dec 1989 |

### Keywords

- container-free systems
- isoperimetric deficit
- Pressure ensemble
- two-dimensional random polytopes

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## Cite this

Bavaud, F. (1989). Statistical mechanics of convex bodies.

*Journal of Statistical Physics*,*57*(5-6), 1059-1068. https://doi.org/10.1007/BF01020048