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    L’abuso dell’abuso e il ricorso improprio alla solidarietà

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    Per verificare la sussistenza di un abuso del diritto, occorre guardare non al singolo potere ma alla piú ampia funzione del rapporto. Diversamente, il rischio è quello di un errato giudizio sulla legittimità dell’esercizio delle situazioni giuridiche soggettive. Il rischio è, cioè, che si abusi dell’abuso

    PDE/Statistical Mechanics Duality: Relation Between Guerra’s Interpolated p-Spin Ferromagnets and the Burgers Hierarchy

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    We examine the duality relating the equilibrium dynamics of the mean-field p-spin ferromagnets at finite size in the Guerra’s interpolation scheme and the Burgers hierarchy. In particular, we prove that—for fixed p—the expectation value of the order parameter on the first side w.r.t. the generalized partition function satisfies the p- 1 -th element in the aforementioned class of nonlinear equations. In the light of this duality, we interpret the phase transitions in the thermodynamic limit of the statistical mechanics model with the development of shock waves in the PDE side. We also obtain the solutions for the p-spin ferromagnets at fixed N, allowing us to easily generate specific solutions of the corresponding equation in the Burgers hierarchy. Finally, we obtain an effective description of the finite N equilibrium dynamics of the p= 2 model with some standard tools in PDE side
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