  Since its inception about two centuries ago thermodynamics has sparkled
continuous interest and fundamental questions. According to the second law no
heat engine can have an efficiency larger than Carnot's efficiency. The latter
can be achieved by the Carnot engine, which however ideally operates in
infinite time, hence delivers null power. A currently open question is whether
the Carnot efficiency can be achieved at finite power. Most of the previous
works addressed this question within the Onsager matrix formalism of linear
response theory. Here we pursue a different route based on finite-size-scaling
theory. We focus on quantum Otto engines and show that when the working
substance is at the verge of a second order phase transition diverging energy
fluctuations can enable approaching the Carnot point without sacrificing power.
The rate of such approach is dictated by the critical indices, thus showing the
universal character of our analysis.
