Ordering of limits in the Jarzynski equality

Steve Presś, Robert Silbey

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We consider the sampling problems encountered in computing free-energy differences using Jarzynski's nonequilibrium work relation [Phys. Rev. Lett. 56, 2690 (1997)]. This relation expresses the free-energy change of a system, on which finite-time work is done, as an average over all possible trajectories of the system. This average can then be expressed as a cumulant expansion of the work. We study the scaling of these cumulants with an appropriately defined measure of phase-space accessibility ε and particle number N for two simple changes in state. We find that the cumulant expansion is slowly convergent for predominantly entropic processes, those where ε is considerably altered during the course of the process. An accurate determination of the free-energy change requires some knowledge of the behavior of the tails of the work distribution associated with the process. Jarzynski's irreversible work relation is only valid with the correct ordering of the infinite limits of N and ε, clarifying the regime of its applicability.

Original languageEnglish (US)
Article number054117
JournalJournal of Chemical Physics
Issue number5
StatePublished - 2006
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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