Clausius inequality for finite baths reveals universal efficiency improvements

We study entropy production in nanoscale devices, which are coupled to finite heat baths. This situation is of growing experimental relevance, but most theoretical approaches rely on a formulation the second law valid only for infinite fix this problem by pointing out that already Clausius' paper from 1865 contains an adequate baths, can be also rigorously derived microscopic quantum description. inequality shows nonequilibrium processes less irreversible than previously thought. use it correctly extend Landauer's principle baths and we demonstrate any engine contact with has higher efficiency Importantly, our results easy study, requiring knowledge average bath energy.