Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski's Equality

TLDR

Recent advances in statistical mechanical theory, including Jarzynski's 1997 equality, show that equilibrium free‑energy differences can be derived from processes far from equilibrium. The study tests Jarzynski's equality by mechanically stretching a single RNA molecule between two conformations. The experiment measures reversible and irreversible work trajectories during mechanical stretching to evaluate the equality. The equality accurately recovers the ΔG profile within kBT/2 of the best independent estimate, demonstrating a bridge between equilibrium and nonequilibrium thermodynamics and extending single‑molecule analysis beyond equilibrium contexts.

Abstract

Recent advances in statistical mechanical theory can be used to solve a fundamental problem in experimental thermodynamics. In 1997, Jarzynski proved an equality relating the irreversible work to the equilibrium free energy difference, Δ G . This remarkable theoretical result states that it is possible to obtain equilibrium thermodynamic parameters from processes carried out arbitrarily far from equilibrium. We test Jarzynski's equality by mechanically stretching a single molecule of RNA reversibly and irreversibly between two conformations. Application of this equality to the irreversible work trajectories recovers the Δ G profile of the stretching process to within k B T /2 (half the thermal energy) of its best independent estimate, the mean work of reversible stretching. The implementation and test of Jarzynski's equality provides the first example of its use as a bridge between the statistical mechanics of equilibrium and nonequilibrium systems. This work also extends the thermodynamic analysis of single molecule manipulation data beyond the context of equilibrium experiments.