### 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 |
---|---|

Pages (from-to) | 477-481 |

Number of pages | 5 |

Journal | Journal of Mathematical Physics |

Volume | 19 |

Issue number | 2 |

Publication status | Published - 1977 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*19*(2), 477-481.

**Exact statistical mechanics of some classical 1D systems.** / Bountis, Tassos; Helleman, Robert H G.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 19, no. 2, pp. 477-481.

}

TY - JOUR

T1 - Exact statistical mechanics of some classical 1D systems

AU - Bountis, Tassos

AU - Helleman, Robert H G

PY - 1977

Y1 - 1977

N2 - The classical partition function QN is calculated in closed form for the following 1D N-body "hard-core" potentials, V = Σ i = 1 N (gxi + b/|xi - x i-1|), i.e., a Coulomb nearest neighbor "chain" in a uniform field, and V = (1/2)Σi = 0 N Σ j = 0 N exp (|xi - xj|), a "fluid" with exponential interactions. The QN 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."

AB - The classical partition function QN is calculated in closed form for the following 1D N-body "hard-core" potentials, V = Σ i = 1 N (gxi + b/|xi - x i-1|), i.e., a Coulomb nearest neighbor "chain" in a uniform field, and V = (1/2)Σi = 0 N Σ j = 0 N exp (|xi - xj|), a "fluid" with exponential interactions. The QN 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."

UR - http://www.scopus.com/inward/record.url?scp=36749106167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749106167&partnerID=8YFLogxK

M3 - Article

VL - 19

SP - 477

EP - 481

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

ER -