Non-reversible Lifts of Reversible Diffusions and Hypocoercivity

We introduce a new concept of lifts of reversible diffusion processes and show that various well-known non-reversible Markov processes arising in applications are lifts in this sense of simple reversible diffusions. Furthermore, we show that non-asymptotic relaxation times can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how quantitative hypocoercivity can be obtained for second-order lifts based on a time-integrated Poincaré inequality, and how this can be applied to find optimal lifts.