Stochastic Thermodynamics

Classical thermodynamics is applicable in a wide range of theoretical and practical systems. One of the key assumptions is, however, that the system is big and a large number of individual particles in involved. When the systems become smaller fluctuations play a crucial role. Examples for such systems range from biochemical networks and proteins to small particles immersed in a water bath. The framework of stochastic thermodynamics extends the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories. As a result derived quantities such as the efficiency can be defined in single particle systems, as for instance for molecular motors. Moreover, the fluctuations in the systems can be further characterized. For instance the fluctuation theorem relates the probabilities of trajectories with negative entropy production with the probability to observe a trajectory with positive entropy production

Thermoelectric engines consist of two heat and particle reservoirs, which are permanently coupled by a conductor. Due to the Seebeck effect, the heat current flowing naturally in this setup can drive a particle current into the same direction thus generating electrical power. During the last decades, substantial efforts have been gone into the miniaturization of both of these types of devices down to micro- and nanometers. On theses small scales, their operation principles can be  scrutinized under the microscope by virtue of precise measurements of characteristic quantities like applied work or exchanged heat. Here, we use the framework of stochastic thermodynamics to investigate the laws that determine the efficiency and power of mesoscopic heat engines. In particular, we are interested in the relation between these two figures and the attainability of the Carnot efficiency, a universal upper bound following from the second law.

Most physical descriptions involve some sort of coarse graining. Particulary in the description of meso or macroscopic systems one needs to deal with hidden fast degrees of freedom such as the myriads of solvent particles that are treated in an effective manner when describing the diffusion of a colloidal particle in the Langevin approach. Generally, an effective description of such unobserved degrees of freedom is justified if there is a clear-cut time-scale separation in the dynamics. Without such a time-scale separation, neglecting hidden slow degrees of freedom naively can lead to inconsistencies. Here, we investigate the role of hidden slow degrees of freedom in the fluctuation theorem for the apparent entropy production one would infer from a reduced set of variables.