Generalized Jarzynski's equality of inhomogeneous multidimensional diffusion processes

TL;DR

This paper rigorously proves a generalized Jarzynski's equality for inhomogeneous multidimensional diffusion processes using the Feynman-Kac formula, extending thermodynamic laws and related equalities to complex systems.

Contribution

It provides a rigorous mathematical proof of the generalized Jarzynski's equality for inhomogeneous multidimensional diffusions, extending previous work to more complex systems.

Findings

Extended Jarzynski's equality to multidimensional inhomogeneous processes

Connected the equality to the second law of thermodynamics

Applied the results to steady state thermodynamics

Abstract

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 ({\em Proc. Natl. Acad. Sci. USA} {\bf 98}(7), 3658--3661 (2001)) and Hatano-Sasa equality of steady state thermodynamics ({\em Phys. Rev. Lett.} {\bf 86}, 3463--3466 (2001)) to the general multidimensional case.