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Abstract

Using the Feynman-Kac formula, a work fluctuation theorem for a Brownian particle in a nonconfining potential, e.g., a potential well with finite depth, is derived. The theorem yields an inequality that puts a lower bound on the average work needed to change the potential in time. In comparison to the Jarzynski equality, which holds for confining potentials, an additional term describing a form of energy related to the never-ending diffusive expansion appears.