From Feynman–Vernon to Wiener stochastic path integral

Abstract We establish a formal connection between the Feynman–Vernon path integral formalism for open quantum systems and the Wiener path integral used in classical stochastic dynamics, further exploring its applications. By considering a generalized influence functional in the strong decoherence limit, we demonstrate that integrating over the quantum coherence length leads to stochastic Langevin dynamics. Specifically, under our model, we show that the quantum Feynman differential transforms into an underdamped multiplicative non-Markovian Langevin dynamics. Applying this framework to the Wigner function representation, we show that the system follows a stochastic path interpretable via classical probability theory, allowing for the investigation of decoherence through classical dynamics. Finally, we address the inverse problem: constructing an equivalent quantum influence functional from a given classical Langevin equation.