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的一种新提升概念，并展示了应用中出现的各类经典不可逆马尔可夫过程在某种意义上均为简单可逆扩散的提升。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可将其减少平方根倍，从而推广了离散时间中的相关结论。最后，我们展示了如何将基于时空庞加莱不等式的定量次指数收敛性最新研究方法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。