### Abstract

The classical partition function Q_{N} is calculated in closed form for the following 1D N-body "hard-core" potentials, V = Σ _{i = 1}^{N} (gx_{i} + b/|x_{i} - x _{i-1}|), i.e., a Coulomb nearest neighbor "chain" in a uniform field, and V = (1/2)Σ_{i = 0}^{N} Σ _{j = 0}^{N} exp (|x_{i} - x_{j}|), a "fluid" with exponential interactions. The Q_{N} for both systems is separated into a product of N, similar, tractable integrals each depending on a different value of the index i. All thermodynamic variables are obtained in closed form. In the limit, as N→∞, most of them do not linearly increase with the size of the system, i.e., they are not "extensive." This is also discussed in terms of the "stability" and "temperedness" properties of the potentials. Nevertheless, both systems do have a heat capacity which is "extensive."

Original language | English |
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Pages (from-to) | 477-481 |

Number of pages | 5 |

Journal | Journal of Mathematical Physics |

Volume | 19 |

Issue number | 2 |

Publication status | Published - Dec 1 1977 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*19*(2), 477-481.