A Statistical Mechanical Approach to the Problem of a Fluid in an External Field
- 1 February 1972
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 13 (2) , 222-226
- https://doi.org/10.1063/1.1665958
Abstract
A rigorous, equilibrium statistical mechanical treatment of a fluid in a weak external field is given. The technique involves a cell division which leads to upper and lower bounds for the free energy density. Under a suitable double limiting procedure these limits coalesce, yielding a free energy consisting of a field‐free term plus a field‐dependent term. The cell division allows a direct physical definition of the local pressure p(s) and the local density ρ(s). This treatment provides a rigorous derivation of the thermodynamics of a fluid in a weak external field and, in particular, the hydrostatic equation gradp = − ρ gradφ.Keywords
This publication has 3 references indexed in Scilit:
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- Convergence of Fugacity Expansions for Fluids and Lattice GasesJournal of Mathematical Physics, 1963