### Abstract

This paper deals with the grand canonical entropy of a lattice gas mixture. The entropy is a function of the multisite densities corresponding to the interaction pattern of the system in question. It is first evaluated for a nearest-neighborinteraction, one-dimensional simple lattice gas to show how the structure of bulk fluid is locally maintained. Generalization requires one set of interrelations among multisite densities presented in closed form for an arbitrary lattice, and one set between Boltzmann factors and multisite densities which is written down for simply connected lattices. Application is made to two-row lattices, which turn out to have local behavior from this viewpoint, as do all single-row or Bethe lattices with complete range-p interactions. Nonlocal examples are also given, and suggestions made for approximation sequences in general lattices.

Original language | English (US) |
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Pages (from-to) | 221-243 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 60 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 1990 |

### Keywords

- Bethe lattice
- Lattice gas
- entropy functional
- mixture
- nonlocal response
- nonneighbor coupling
- nonuniform fluid

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Journal of Statistical Physics*,

*60*(1-2), 221-243. https://doi.org/10.1007/BF01013675