Integral equations and inequalities in the theory of fluids

Journal Article · Sun Dec 01 04:00:00 EST 1963 · Journal of Mathematical Physics (New York) (U.S.)

DOI:https://doi.org/10.1063/1.1703930· OSTI ID:4148648

Lebowitz, J L; Percus, J K

Using the method of functional Taylor expansion develope previously, and 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 Krikwood-Salsburg equations. By terminating the Taylor expansion after a finite number of terms and retaining the remainder, inequalities are also obtained for the distribution functions and thermodynamic parameters of the fluid. For the case of positive interparticle potentials, the inequalities first found by Lieb are recovered. For nonpositive potentials, new inequalities (some also obtained by Penrose) are derived. These inequalities are applied to the case of a hardsphere 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.

• Research Organization: Yeshiva Univ., New York
• NSA Number: NSA-18-002432
• OSTI ID: 4148648
• Journal Information: Journal of Mathematical Physics (New York) (U.S.), Journal Name: Journal of Mathematical Physics (New York) (U.S.) Vol. Vol: 4; ISSN JMAPA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ATOMS
BOSONS
COMPUTERS
DIFFERENTIAL EQUATIONS
DISTRIBUTION
ELECTRONS
ENERGY
ENERGY LEVELS
EQUATIONS
FERMIONS
FLUIDS
GASES
HARTREE APPROXIMATION
INTEGRAL EQUATIONS
INTEGRALS
INTERACTIONS
MANY BODY PROBLEM
MATHEMATICS
MECHANICS
PARTICLES
PERTURBATION THEORY
PRESSURE
QUANTUM MECHANICS
SELF-CONSISTENT FIELD
SPHERES
STATISTICS
THERMODYNAMICS
VARIATIONAL METHOD