Advances in technology so far have enabled us to downsize heat engines, and current state-of-the-art experiments have reached the stage to realize heat engines with a single colloidal particle or macromolecule [1], where fluctuations in thermodynamic quantities are non negligible [2]. To characterize the performance of such microscopic heat engines, it is essentially important to go beyond the description by mean values as in the conventional thermodynamics for macroscopic systems, and capture their higher-order statistical properties.
We attack this issue of microscopic heat engines [3]. Namely, we study the higher-order statistical properties of the Carnot cycle whose working substance consists of a small, classical system. We show that the ratio between the fluctuations of work and heat is given by an universal form depending solely on the temperature ratio between the hot and cold heat baths. Moreover, we show that the Carnot cycle provides the upper bound on this fluctuation ratio for cycles consisting of quasistatic strokes. These results serve as a guiding principle in the design and optimization of fluctuations in small heat engines.