An Isaac Newton Institute Workshop

First-Passage and Extreme Value Problems in Random Processes

The Unreasonable effectiveness of equilibrium-like theory for interpreting non-equilibrium experiments

26th June 2006

Author: Astumian, R (University of Maine)

Abstract

There has been great interest in applying the results of statistical mechanics to single molecule experiements. Recent work has highlighted so-called non-equilibrium work-energy relations and Fluctuation Theorems that take on an equilibrium-like (time independent) form. Here I give a very simple heuristic example where an equilibrium result (the barometric law for colloidal particles) arises from theory describing the {\em thermodynamically} non- equilibrium phenomenon of a single colloidal particle falling through solution due to gravity. This simple description arises from the fact that the particle, even while falling, is in {\em mechanical} equilibrium (gravitational force equal the viscous drag force) at every instant. The results are generalized using Onsager's least dissipation approach for stochastic processes to derive time independent equations that hold for thermodynamically non-equilibrium (and even non-stationary) systems. These equations offer great possibilities for rapid determination of thermodynamic parameters from single molecule experiments.