TOPICS
Thermodynamics of Quantum Devices. Classical thermodynamics was once developed as a phenomenological theory of work and heat to describe and optimize the operation cycles of macroscopic machines such as Otto engines or household refrigerators. In recent years, a new era has begun, in which miniaturization is explored as a novel design principle for thermal devices. Heat engines and refrigerators can now be implemented on atomistic scales, where the rules of classical mechanics no longer apply. In the quantum world, particles can occupy two places at the same time, tunnel through barriers and influence each other at a distance without interaction. These striking phenomena are manifestations of the quantum laws of motion. They enable the design of thermal devices with radically new features, which could eventually overcome the limitations of their classical counterparts.
Our aim is to explore the fundamental principles that govern the dynamics and performance of quantum thermal devices far from equilibrium. We are thereby interested in both the general theory and specific setups that can be experimentally realized through presentday quantum engineering. Combing methods from quantum thermodynamics, the theory of open quantum systems and dynamical control theory, we are searching for new strategies to exploit quantum phenomena in order to enhance the power, efficiency and operational precision of thermal machines.
Thermodynamics of Ballistic Transport. In macroscopic systems at high temperature, transport is a stochastic process, where particles undergo ceaseless collisions that randomly change their velocity and direction of motion. Reducing the temperature of a conductor increases the average distance that a particle can travel between two collisions. Ballistic, or coherent, transport sets in when this mean free path becomes comparable to the dimensions of the sample. In this regime the transfer of particles through the system is governed by the reversible laws of Hamiltonian or quantum mechanics while irreversible processes occur in external reservoirs.
Scattering theory provides an elegant method and physically transparent to describe the thermodynamics of ballistic conductors. As a key result, this approach leads to a direct link between the microscopic properties of the sample and thermodynamic observables like electric currents and entropy production. Here, we use this theoretical framework to investigate the interplay between dissipation, quantum and thermal fluctuations in smallscale conductors and to explore the basic principles that govern the performance and precision of currentdriven nanodevices such as thermoelectric generators and refrigerators.
Related Publications:

K. Brandner, K. Saito Thermodynamic Geometry of Microscopic Heat Engines, Phys. Rev. Lett. 124 040602 (2020).

P. Menczel, K. Brandner Limit cycles in periodically driven open quantum systems, J. Phys. A: Math. Theor. 52 43LT01 (2019).

P. Menczel, T. Pyhäranta, C. Flindt, K. Brandner Twostroke optimization scheme for mesoscopic refrigerators, Phys. Rev. B 99, 224306 (2019).

E. Potanina, K. Brandner, C. Flindt Optimization of quantized charge pumping using full counting statistics, Phys. Rev. B 99, 035437 (2019).

K. Brandner, M. Bauer, U. Seifert Universal CoherenceInduced Power Losses of Quantum Heat Engines in Linear Response, Phys. Rev. Lett. 119, 170602 (2017).

K. Brandner, U. Seifert Periodic thermodynamics of open quantum systems, Phys. Rev. E 93, 062134 (2016).

M. Bauer, K. Brandner, U. Seifert Optimal performance of periodically driven, stochastic heat engines under limited control, Phys. Rev. E 93, 042112 (2016).

K. Brandner, K. Saito, U. Seifert Thermodynamics of Micro and NanoSystems Driven by Periodic Temperature Variations, Phys. Rev. X 5, 031019 (2015).

K. Brandner, M. Bauer, M. T. Schmid, U. Seifert Coherenceenhanced efficiency of feedbackdriven quantum engines, New J. Phys. 17, 065006 (2015).
Related Publications:

K. Macieszczak, K. Brandner, J. P. Garrahan Unified Thermodynamic Uncertainty Relations in Linear Response, Phys. Rev. Lett. 121 130601 (2018).

K. Brandner, T. Hanazato, K. Saito Thermodynamic Bounds on Precision in Ballistic Multiterminal Transport, Phys. Rev. Lett. 120, 090601 (2018).

K. Brandner, U. Seifert, Bound on thermoelectric power in a magnetic field within linear response, Phys. Rev. E 91, 012121 (2015).

J. Stark, K. Brandner, K. Saito, U. Seifert Classical Nernst engine, Phys. Rev. Lett. 112, 140601 (2014).

K. Brandner, U. Seifert, Multiterminal thermoelectric transport in a magnetic field: bounds on Onsager coefficients and efficiency, New J. Phys. 15, 105003 (2013).

K. Brandner, K. Saito, U. Seifert, Strong Bounds on Onsager Coefficients and Efficiency for ThreeTerminal Thermoelectric Transport in a Magnetic Field, Phys. Rev. Lett. 110, 070603 (2013).
LeeYang Zeros. Phase transitions like the condensation of a gas into a liquid at a critical temperature are determined by large fluctuations of thermodynamic observables and an anomalous behavior of the free energy. More than half a century ago, Lee and Yang realized that these exceptional features can be understood from the complex values of the external control parameter, e.g. temperature, at which the partition function of a small system vanishes; in the thermodynamic limit, these LeeYang zeros approach the critical point on the real axis. Over the last decades, this groundbreaking idea has lead to a powerful theoretical framework that covers not only conventional but also nonequilibrium and dynamical phase transitions.
In this line of research, we are investigating the laws that determine the trajectories of LeeYang zeros in the complex plane and their relation to physical quantities like the highorder cumulants of a stochastic process, which can be directly observed in experiments. Applying tools from largedeviation theory, we recently showed that the complex LeeYang zeros can be used to infer the behaviour of a system in the thermodynamic limit from its fluctuations in the smallsize regime. Further exploring the generality and consequences of this result, which suggests a quite remarkable duality between small and large systems, is a goal of our research.
Related Publications:

A. Deger, K. Brandner, C. Flindt LeeYang zeros and largedeviation statistics of a molecular zipper, Phys. Rev. E 97, 012115 (2018).

K. Brandner, V. F. Maisi, J. P. Pekola, J. P. Garrahan, C. Flindt Experimental Determination of Dynamical LeeYang Zeros, Phys. Rev. Lett. 118, 180601 (2017).