Abstract
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."
| 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 |
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ASJC Scopus subject areas
- Organic Chemistry
Cite this
Exact statistical mechanics of some classical 1D systems. / Bountis, Tassos; Helleman, Robert H G.
In: Journal of Mathematical Physics, Vol. 19, No. 2, 1977, p. 477-481.Research output: Contribution to journal › Article
}
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."
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M3 - Article
VL - 19
SP - 477
EP - 481
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 2
ER -