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