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：原文摘要：我们提出了一种可逆扩散过程提升的新概念，并证明应用中出现的各种经典非可逆马尔可夫过程在某种意义上正是简单可逆扩散过程的这种提升。此外，我们引入了非渐近松弛时间的概念，并证明通过提升最多只能将这类时间缩短一个平方根的量级，从而推广了离散时间下的相关结论。最后，我们阐释了基于时空庞加莱不等式的定量次规范收敛性方法如何能够用提升的语言重新表述并简化，以及如何应用该方法寻找最优提升。