Practical applicability of the jarzynski relation in statistical mechanics: A pedagogical example

Rhonald C. Lua, Alexander Y. Grosberg

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We suggest and discuss a simple model of an ideal gas under the piston to gain an insight into the workings of the Jarzynski identity connecting the average exponential of the work over the nonequilibrium trajectories with the equilibrium free energy. We show that the identity is valid for our system, due to the very rapid molecules belonging to the tail of the Maxwell distribution. For the most interesting extreme, when the system volume is large, while the piston is moving with great speed (compared to thermal velocity) for a very short time, the necessary number of independent experimental runs to obtain a reasonable approximation for the free energy from averaging the nonequilibrium work grows exponentially with the system size.

    Original languageEnglish (US)
    Pages (from-to)6805-6811
    Number of pages7
    JournalJournal of Physical Chemistry B
    Volume109
    Issue number14
    DOIs
    StatePublished - Apr 14 2005

    ASJC Scopus subject areas

    • Physical and Theoretical Chemistry
    • Surfaces, Coatings and Films
    • Materials Chemistry

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