Nonlinear Thermodynamic Formalism: Mean-field Phase Transitions, Large Deviations and Bogoliubov's Variational Principle

Jean-Bernard Bru, Walter de Siqueira Pedra, Artur O. Lopes

Let $\hat{I}\text{c◯}=\{1,2,\dots ,d{\}}^{\mathbb{N}}$, $T$ be the shift acting on $\hat{I}\text{c◯}$, $\mathcal{P}(T)$ the set of $T$-invariant probabilities. Given a Hölder potential $A$ and a continuous fu…