The Jarzynski identity: lessons from the Random Energy model

by Prof. Matteo Palassini (Barcelona)

Wednesday 21 May 2008, 10:00 → 11:00 Europe/Stockholm

Nordita Seminar Room

The Jarzynski identity provides a method for estimating free-energy differences from nonequilibrium work measurements. In practice, however, this estimator is affected by a large bias due to exponential averaging. Motivated by this, we consider the problem of estimating , where Z is the sum of quantities exp(X_i) and the X_i are i.i.d. random variables. In the appropriate scaling limit, this gives the free-energy of the Random Energy Model. We compute analytically the finite-size corrections to in different regimes. For small n (corresponding to the glassy phase of the REM), we extend known results for the REM with gaussian-distributed X_i to a more general distribution, and confirm the results with an extreme-value approach. For large n, we use a replica symmetry breaking approach. We show that the analytical results describe well the Jarzynski estimator for the typical work values of single-molecule pulling experiments, and we discuss how one may devise improved estimators based on these results.