Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 131, Issue 4, Pages 675-689Publisher
SPRINGER
DOI: 10.1007/s10955-008-9520-4
Keywords
Feynman-Kac formula; Jarzynski's equality; inhomogeneous diffusion processes; nonequilibrium thermodynamics; Hatano-Sasa equality
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Applying the well-known Feynman-Kac formula of inhomogeneous case, an interesting and rigorous mathematical proof of generalized Jarzynski's equality of inhomogeneous multidimensional diffusion processes is presented, followed by an extension of the second law of thermodynamics. Then, we explain its physical meaning and applications, extending Hummer and Szabo's work (Proc. Natl. Acad. Sci. USA 98(7):3658-3661, [2001]) and Hatano-Sasa equality of steady state thermodynamics (Phys. Rev. Lett. 86:3463-3466, [2001]) to the general multidimensional case.
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