Convergence Properties and Ordering of Limits in Jarzynski's Nonequilibrium Work Relation
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
We consider the convergence problems encountered in computing free energy
differences using Jarzynski's nonequilibrium work relationPhys.Rev.Lett. 56,
2690(1997). This relation expresses the free energy change of a system, on
which finite time work is done, as a sum over work cumulants. We study the
scaling of these cumulants with an appropriately defined measure of phase
space accessibility, x, and particle number, N, for model systems. It is shown
that the work relation is in principle slowly convergent for entropic processes
and that a correct ordering of the limits of x and N clarifies the regime of
practical applicability of this equality. We also discuss a) the phenomenon of work distribution broadening arising from system-bath interaction and finite-system recurrences, b) when a stochastic treatment of the dynamics may be legitimately invoked and c)how information on the system-bath interaction may be extracted from work distributions. We conclude with a note on stretching
floppy polymer systems.