### Abstract

Using the method of functional Taylor expansion developed previously, an extensive set of equations is obtained for the distribution functions and Ursell functions in a classical fluid. These include in a systematic way many previously derived relations, e.g., Mayer-Montroll and Kirkwood-Salsburg equations. By terminating the Taylor expansion after a finite number of terms and retaining the remainder, we also obtain inequalities for the distribution functions and thermodynamic parameters of the fluid. For the case of positive interparticle potentials, we recover the inequalities first found by Lieb. For nonpositive potentials, new inequalities (some also obtained by Penrose) are derived. These inequalities are applied to the case of a hard-sphere fluid in three dimensions where they are compared with the results of machine computations and approximate theories. Different inequalities, not obtainable from the above considerations, and some properties of the fugacity expansions, are also derived.

Original language | English (US) |
---|---|

Pages (from-to) | 1495-1506 |

Number of pages | 12 |

Journal | Journal of Mathematical Physics |

Volume | 4 |

Issue number | 12 |

State | Published - 1963 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*4*(12), 1495-1506.

**Integral equations and inequalities in the theory of fluids.** / Lebowitz, J. L.; Percus, Jerome.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 4, no. 12, pp. 1495-1506.

}

TY - JOUR

T1 - Integral equations and inequalities in the theory of fluids

AU - Lebowitz, J. L.

AU - Percus, Jerome

PY - 1963

Y1 - 1963

N2 - Using the method of functional Taylor expansion developed previously, an extensive set of equations is obtained for the distribution functions and Ursell functions in a classical fluid. These include in a systematic way many previously derived relations, e.g., Mayer-Montroll and Kirkwood-Salsburg equations. By terminating the Taylor expansion after a finite number of terms and retaining the remainder, we also obtain inequalities for the distribution functions and thermodynamic parameters of the fluid. For the case of positive interparticle potentials, we recover the inequalities first found by Lieb. For nonpositive potentials, new inequalities (some also obtained by Penrose) are derived. These inequalities are applied to the case of a hard-sphere fluid in three dimensions where they are compared with the results of machine computations and approximate theories. Different inequalities, not obtainable from the above considerations, and some properties of the fugacity expansions, are also derived.

AB - Using the method of functional Taylor expansion developed previously, an extensive set of equations is obtained for the distribution functions and Ursell functions in a classical fluid. These include in a systematic way many previously derived relations, e.g., Mayer-Montroll and Kirkwood-Salsburg equations. By terminating the Taylor expansion after a finite number of terms and retaining the remainder, we also obtain inequalities for the distribution functions and thermodynamic parameters of the fluid. For the case of positive interparticle potentials, we recover the inequalities first found by Lieb. For nonpositive potentials, new inequalities (some also obtained by Penrose) are derived. These inequalities are applied to the case of a hard-sphere fluid in three dimensions where they are compared with the results of machine computations and approximate theories. Different inequalities, not obtainable from the above considerations, and some properties of the fugacity expansions, are also derived.

UR - http://www.scopus.com/inward/record.url?scp=0009297795&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009297795&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0009297795

VL - 4

SP - 1495

EP - 1506

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

ER -