Geodesic
Thermodynamics and Hydrodynamics (Statistical Foundations): 2. Thermodynamic Equilibrium
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 2, pp. 325-336

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We show that the BBGKY hierarchy in thermodynamic equilibrium degenerates into an equilibrium hierarchy. In turn, the latter can be used to obtain both the fundamental system of equations describing the state of matter inside a correlation sphere of the radius $R\approx10^{-7}$cm and the canonical Gibbs distribution, which, according to the current concepts, describes the state of the entire macroscopic system. We show that the Gibbs distribution is indeed also local, i.e., describes the state of matter only inside the correlation sphere; in the thermostat surrounding this sphere, the Gibbs distribution degenerates into a constant. We state that these two approaches are equivalent to each other.
Keywords: equilibrium BBGKY hierarchy, local approach, Gibbs distribution, Ornstein–Zernike equation, correlation sphere, thermostat. 
@article{TMF_2003_134_2_a11,
     author = {G. A. Martynov},
     title = {Thermodynamics and {Hydrodynamics} {(Statistical} {Foundations):} 2. {Thermodynamic} {Equilibrium}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {325--336},
     publisher = {mathdoc},
     volume = {134},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a11/}
}
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G. A. Martynov. Thermodynamics and Hydrodynamics (Statistical Foundations): 2. Thermodynamic Equilibrium. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 2, pp. 325-336. http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a11/