Quantum Brownian motion for embedded system

Abstract Conventional derivations of the Wigner phase-space Fokker–Planck equation for open quantum systems often rely on heuristic coarse-graining of system-bath interactions. We present quantum dissipation in a minimally extended state space (QD-MESS), a unified framework that systematically models Gaussian bath dynamics in Wigner phase space with controllable numerical accuracy, yields a transparent quantum-classical picture for arbitrary noise spectra, and recovers the quantum-optical, Caldeira–Leggett, and quantum Smoluchowski limits.