Equidistant quenches in few-level quantum systems

Recently it was shown that, if we consider overdamped diffusive systems and a pair of \textit{thermodynamically} equidistant quenches, from a colder and a hotter temperature to a fixed ambient temperature, the relaxation process is asymmetric and the relaxation from the colder initial temperature to the ambient temperature (\textit{uphill} relaxation) is always faster compared to the relaxation from the warmer initial temperature to the ambient temperature (\textit{downhill} relaxation) for dynamics close to a stable minima [Phys. Rev. Lett. 125, 110602]. Here we investigate whether similar results hold in open quantum systems with a few energy levels, and check whether the results depend on the choice of the distance measure. For two level systems, we also look at the effect of coherences in the initial state. The new results provide insights into understanding the results in [Phys. Rev. Lett. 125, 110602] as the continuum limit of discrete space systems.