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Abstract

The fluctuations of dynamical functionals such as the empirical density and current as well as heat, work and generalized currents in stochastic thermodynamics are often studied within the Feynman-Kac tilting formalism, which in the physics literature is typically derived by some form of Kramers-Moyal expansion. Here we derive the Feynman-Kac theory for general additive dynamical functionals directly via Itô calculus and via functional calculus, where the latter approach in fact appears to be new. Using Dyson series we then independently recapitulate recent results on steady-state (co)variances of general additive dynamical functionals derived
in arXiv:2105.10483 and arXiv:2204.06553 directly from Itô calculus avoiding any tilting.
We hope for our work to put the different approaches to stochastic functionals employed in the field on a common footing.