Thermodynamics at the microscale: from effective heating to the Brownian Carnot engine

We review a series of experimental studies of the thermodynamics of nonequilibrium processes at the microscale. In particular, in these experiments we studied the fluctuations of the thermodynamic properties of a single optically-trapped microparticle immersed in water and in the presence of external random forces. In equilibrium, the fluctuations of the position of the particle can be described by an effective temperature that can be tuned up to thousands of Kelvins. Isothermal and non-isothermal thermodynamic processes that also involve changes in a control parameter were implemented by controlling the effective temperature of the particle and the stiffness of the optical trap. Since truly adiabatic processes are unfeasible in colloidal systems, mean adiabatic protocols where no average heat is exchanged between the particle and the environment are discussed and implemented. By concatenating isothermal and adiabatic protocols, it is shown how a single-particle Carnot engine can be constructed. Finally, we provide an in-depth study of the fluctuations of the energetics and of the efficiency of the cycle.