Universal attainment of Carnot efficiency at finite power with critical heat engines

Michele Campisi, Rosario Fazio

Published 2016-03-16Version 1

Since its inception about two centuries ago thermodynamics has sparkled continuous interest and fundamental questions. According to the second law no heat engine working between two heat reservoirs at temperatures $T_1>T_2$ can have an efficiency larger than Carnot's efficiency $\eta^C = 1-T_2/T_1$. The latter can be achieved by the Carnot engine, which however ideally operates in infinite time, hence delivers null power. A question that is currently in the limelight of current investigation 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 the asymptotic approach towards the Carnot point at finite power. The rate of such approach is dictated by the critical indices, thus showing the universal character of our analysis.