Relativistic Langevin equation derived from a particle-bath Lagrangian

Abstract We show how a relativistic Langevin equation can be derived from Lorentz-covariant version of the Caldeira–Leggett particle-bath Lagrangian. In one its limits, we identify obtained with used in contemporary extensions statistical mechanics to near-light-speed motion tagged particle non-relativistic dissipative fluids. The proposed framework provides more rigorous and first-principles form weakly-relativistic partially-relativistic equations often quoted or postulated as ansatz previous works. then refine aforementioned results obtain generalized valid for case both fully-relativistic bath, using an analytical approximation numerics where Fourier modes bath are systematically replaced covariant plane-wave forms length-scale correction that depends on space-time trajectory parabolic way. A new force term appears this limit, which has been here first time. discuss implications apparent breaking translation parity invariance, showing these effects not necessarily contradiction assumptions mechanics. intrinsically non-Markovian character fully generalised here, associated fluctuation–dissipation theorem, is also discussed.