This talk is concerned with freezing phase transitions in general dynamical systems. A freezing phase transition is one in which, for a given potential $\phi$, there exists some inverse temperature $\beta_0 > 0$ such that for all $\alpha, \beta > \beta_0$, the collection of equilibrium states for $\alpha \phi$ and $\beta \phi$ 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