Department of Chemistry Seminar - Dima Makarov

What’s in common between the position of a molecular motor moving along its track and the content of one’s wallet? Both undergo some sort of (biased) random walk, whose properties depend on random interactions with the environment.  In this talk I will discuss two connected problems. The first is concerned with, arguably, the most interesting stage of a chemical reaction where the molecule is crossing an activation barrier. While in transit, the molecule can be thought of as a player in the “gambler’s ruin” game, with the reactant and product states corresponding to going broke and winning (or the other way around). I will argue that the “rules” of this game, which are discoverable via single-molecule measurements, contain information far beyond phenomenological equations of chemical kinetics.    

The second problem is inspired by John Stanton’s “money game”, which many of us use to teach the Boltzmann distribution in a physical chemistry class. I will show how “unfair” extensions of this game that break time-reversal symmetry result in the famous Pareto distribution of wealth; in contrast, fair, equilibrium, time-reversible exchange games, just like random molecular collisions in a gas, universally lead to Boltzmann statistics.