Fluctuations in heat engines

Abstract

At the dawn of thermodynamics, Carnot's constraint on efficiency of heat engines stimulated the formulation of one of the most universal physical principles, the second law of thermodynamics. In recent years, the field of heat engines acquired a new twist due to enormous efforts to develop and describe microscopic machines based on systems as small as single atoms. At microscales, fluctuations are an inherent part of dynamics and thermodynamic variables such as work and heat fluctuate. Novel probabilistic formulations of the second law imply general symmetries and limitations for the fluctuating output power and efficiency of the small heat engines. Will their complete understanding ignite a similar revolution as the discovery of the second law? Here, we review the known general results concerning fluctuations in the performance of small heat engines. To make the discussion more transparent, we illustrate the main abstract findings on exactly solvable models and provide a thorough theoretical introduction for newcomers to the field.