We propose 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 introduce a concept of non-asymptotic relaxation times and show that these can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how the recently developed approach to quantitative hypocoercivity based on space-time Poincar\'e inequalities can be rephrased and simplified in the language of lifts and how it can be applied to find optimal lifts.

翻译：我们提出了可逆扩散过程提升的新概念，并证明应用中出现的多种经典不可逆马尔可夫过程在某种意义上都是简单可逆扩散过程的这类提升。此外，我们引入非渐近弛豫时间的概念，并证明通过提升，这些弛豫时间最多只能减少平方根倍，从而推广了离散时间下的相关结论。最后，我们展示了基于时空庞加莱不等式发展起来的定量亚松弛方法如何用提升语言重新表述并简化，以及如何将其应用于寻找最优提升。