Flaw of Jarzynski's equality when applied to systems with several degrees of freedom

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Simple example: During the sudden expansion of an isolated ideal gas from a small volume V_0 into a larger one V_1, the entropy changes by Delta S= N ln(V_1/V_0)=-beta Delta F>0 but no work W is produced nor absorbed. Consequently, Jarzynski's identity <exp(-beta W)>= exp(-beta Delta F) is wrong.
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