Mixing is hugely important to a bartender. What happens when they stir your drink? A dynamical system, of course. How do they know when the drink is sufficiently mixed? Well when you reach an equilibrium state, of course. We can abstractify these ideas and create a huge area of ergodic theory known as the thermodynamic formalism. We’ll look at some not-so-trivial measures (and some trivial ones) and create a general class of so called “equilibrium state measures” using a magical theorem of Ruelle, Perron and Frobenius. And we can test all of these ideas out with a nice cocktail at Sandbar afterwards!