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We study two non-equilibrium work fluctuation theorems, the Crooks' theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled.
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In the presence of a field which breaks time-reversal symmetry (such as a magnetic field) equivalent theorems may be derived where one reverses the direction of the field during the backward protocol
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Note that Eq. 9
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The effect of local heating is expected to be largest in 1D, since heat diffuses less effectively than in higher dimensions
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