08 Fakultät Mathematik und Physik

Ever since James Watt's steam engine, the urge to explore the fundamental principles governing the performance of devices that convert thermal energy into useful work was one of the major quests in thermodynamics. From a conceptual point of view, such heat engines can be divided into two classes. Cyclic engines use a reciprocating piston to generate mechanical work by periodically compressing and expanding a working fluid at varying temperature. 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. Over the last decades, substantial efforts have gone into the miniaturization of both 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. In this thesis, we use the framework of stochastic thermodynamics to investigate the laws that determine the efficiency and power of mesoscopic heat engines in the linear response regime. By using primarily algebraic methods, we obtain three major results. First, we show for the paradigmatic class of multi-terminal thermoelectric heat engines that current conservation implies stronger bounds on the efficiency than the bare second law. These bounds become successively weaker as the number of involved terminals increases. Second, we prove a universal bound on the power of multi-terminal engines, which is a quadratic function of their efficiency and does not depend on model-specific parameters like the number of terminals. In particular, this result rules out the option of Carnot efficiency at finite power, which the laws of thermodynamics would, in principle, allow as Benenti et al. recently pointed out [Phys. Rev. Lett. 106, 230602 (2011)]. Finally, after developing a universal framework for the thermodynamic description of periodically driven systems, as our third main result, we show that the same efficiency-dependent bound on power holds for cyclic micro- and nano heat engines, which obey a Fokker-Planck-type dynamics. Our results constitute a significant step towards a better understanding of heat to work conversion on small scales and reveal an intriguing similarity between cyclic and thermoelectric heat engines. Whether this analogy suggests the existence of a so-far-undiscovered universal principle that applies to both types of devices and leads to a bound on power for any heat engine operating in linear response remains an exciting topic for future research.

A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that this additional energetic cost leads to a stronger bound on the work extractable after a single measurement from a system initially in thermal equilibrium (2009 Phys. Rev. A 80 012322). Here, we extend this bound to a large class of feedback-driven quantum engines operating periodically and in finite time. The bound thus implies a natural definition for the efficiency of information to work conversion in such devices. For a simple model consisting of a laser-driven two-level system, we maximize the efficiency with respect to the observable whose measurement is used to control the feedback operations. We find that the optimal observable typically does not commute with the Hamiltonian and hence would not be available in a classical two level system. This result reveals that periodic feedback engines operating in the quantum realm can exploit quantum coherences to enhance efficiency.

08 Fakultät Mathematik und Physik

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