An inherent feature of small systems in contact with thermal reservoirs, be it a pollen grain in water, or an active microbe flagellum, is fluctuations. Even with advanced microscopic techniques, distinguishing active, non-equilibrium processes defined by a constant dissipation of energy to the environment from passive, equilibrium processes is a very challenging task and a vastly developing field of research. For small (microscopic) systems in contact with thermal reservoirs, the experimental / theoretic framework that addresses these fundamental questions, is called stochastic thermodynamics.

In this thesis, we study the stochastic thermodynamics of microscopic machines with colloidal particles as working substances. In particular, we use a path integral based framework to characterize the fluctuations of thermodynamic observables, such as Work, Heat and Entropy production in colloidal heat engines. We obtain exact analytic solutions at finite operational times and the results reveal model independent features of Work and Efficiency fluctuations.

We also discuss the thermodynamic uncertainty relations, which relate current fluctuations in non-equilibrium steady states to the average rate of entropy production. Based on this relation, as well as exact analytical solutions for explicit models, we propose a simple and effective way to infer dissipation from current fluctuations in non-equilibrium systems, from short empirical trajectories.

Finally, we conclude with a discussion on possible extensions of our results.