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On the existence and continuity of the pressure in quantum statistical mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 14 (1973) no. 2, pp. 211-219 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that in the case of all three statistics (Maxwell–Boltzmann; Bose–Einstein, and Fermi–Dirac) the pressure in the canonical ensemble is a continuous function that satisfies a Lipschitz condition provided the pair interaction potential $\Phi(r)$ for $r\eqslantgtr a$ ($a\eqslantgtr0$ is the hardcore radius) is a twice continuously differentiable function. Apart from the usual conditions needed to ensure the existence of the thermodynamic limit, this function satisfies for some $\varepsilon>0$ the further inequality $$ \tilde U_N(x_1,x_2,\dots,x_N)=\sum_{i<j}\tilde{\Phi}(|x_i-x_j|)\eqslantgtr-\tilde BN,\quad\tilde B\eqslantgtr0, $$ where $\tilde{\Phi}(r)=\Phi(r)+\varepsilon(2r\Phi'(r)-r^2\Phi''(r)).$ Some sufficient conditions to be imposed on $\Phi(r)$ for this inequality to hold are given. 
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     author = {L. A. Pastur},
     title = {On the existence and continuity of the pressure in quantum statistical mechanics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {211--219},
     year = {1973},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_14_2_a6/}
}
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L. A. Pastur. On the existence and continuity of the pressure in quantum statistical mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 14 (1973) no. 2, pp. 211-219. http://geodesic.mathdoc.fr/item/TMF_1973_14_2_a6/

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