Experimental test of ensemble inequivalence and the fluctuation theorem in the force ensemble in DNA pulling experiments

We experimentally test the validity of the Crooks fluctuation theorem (CFT) in the force ensemble by pulling DNA hairpins, first with magnetic tweezers, next with optical tweezers using force feedback. The CFT holds when using the definition of work W-f = - integral xdf, where x is the molecular extension and f is the force. In contrast, it does not hold when using the usual definition, appropriate for the constant extension ensemble, W-x = integral f dx, showing the importance of the contribution of boundary terms to the full entropy production in a clear example of statistical ensemble inequivalence in small systems. We also evaluate the differences in the average dissipated work in the force ensemble as compared to the extension ensemble, highlighting ensemble inequivalence also at the level of molecular kinetics.