This talk is concerned with freezing phase transitions in general dynamical systems. A freezing phase transition is one in which, for a given potential $\varphi$, there exists some inverse temperature ${\beta }_0>0$ such that for all $\alpha ,\beta >{\beta }_0$, the collection of equilibrium states for $\alpha \varphi$ and $\beta \varphi$ coincide. In this sense, below the temperature $1/{\beta }_0$, the system “freezes” on a fixed collection of equilibrium states.

We will provide an overview of this direction of study, and conclude with some novel results related to the obtainability of a given measure as a freezing state, as well as the fact that the collection of potentials that freeze is dense in $C(X)$ under certain conditions on the dynamical system.

Reference: https://arxiv.org/abs/2412.05639