Jarzynski's Identity
نویسنده
چکیده
Jarzynski’s identity relates the equilibrium free energy difference ∆F to the work W carried out on a system during a non-equilibrium transformation. In physics literature, the identity is usually written in the form: 〈e−βW 〉 = e−β∆F , where the average is said to be taken over all trajectories in the phase space. The identity in this form has been derived in different ways and published by many authors ([1], [2], [3], [4], [5]). Since the identity involves taking an “average over trajectories”, it is natural to interpret this average as the expectation relative to a probability measure on trajectories, while assuming that the system evolves stochastically. In the present work, Jarzynski’s identity is formulated and proved mathematically rigorously. It is written in the form E[e−βW ] = e−β∆F , where E is the expectation relative to a probability measure on phase space paths. For this probability measure, some analytical assumptions under which Jarzynki’s identity holds are found.
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تاریخ انتشار 2008