The Jarzynski identity: lessons from the Random Energy model
by
Prof.Matteo Palassini(Barcelona)
→
Europe/Stockholm
Nordita Seminar Room
Nordita Seminar Room
Description
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.
