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Quantum Systems out of Equilibrium

Thermodynamics and Collective Phenomena


Kay Brandner

Principal Investigator

Cecilia De Fazio 

Post-doctoral Research Fellow

Joshua Eglinton

PhD Student


Thomas Veness

Post-doctoral Research Fellow


Benjamin Morris

EPSRC Doctoral Prize Holder



Overview. Our subjects of interest are (mostly) quantum systems such as cold atoms, superconducting circuits or mesoscopic conductors that are driven away from equilibrium. We use theoretical models to explore the behavior of these systems from a thermodynamic perspective with special emphasis on the role of collective phenomena that emerge through interactions between many degrees of freedom. The overarching goal of our research is to help laying the theoretical groundwork for the development of small-scale thermodynamic devices that can be applied in quantum and nano-technologies to generate electric or motive power, provide cooling or recover waste heat.  


Quantum Thermal Devices. Classical thermodynamics was developed as a phenomenological theory that describes the equilibrium states of matter and transitions between them on the basis of two fundamental laws. This theory makes it possible to characterize and optimize the operation cycles of macroscopic machines that use or generate heat fluxes such as heat engines and refrigerators. For applications in quantum technologies, such thermal devices must be realized on mesoscopic and atomistic length and energy scales. The modelling of these devices  requires entirely new theoretical methods that are applicable far from equilibrium and account for strong thermal and quantum fluctuations. This framework is provided by stochastic and quantum thermodynamics.


The performance of quantum thermal devices is determined by  a few figures of merit like efficiency, power and precision. A key aim of our work is to develop a comprehensive picture of the relationships between these figures and universal bounds that constrain them.

To explore the practical performance limits of quantum thermal devices, we use general models and methods from optimal control theory to find driving protocols that maximize their figures of merit. At the same time, we search for new mechanisms of energy conversion that exploit collective effects in many-body systems to enhance the output of thermal machines and investigate possible ways to connect them with other quantum technologies.

Quantum Transport Devices. In macroscopic conductors 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 consecutive collisions. Quantum transport sets in when this mean free path becomes comparable to the dimensions of the sample. In this regime, the transport of matter is governed by the laws of quantum mechanics, which give rise to new phenomena such as current quantization and coherent conductance oscillations.


Using scattering theory as our main tool, we investigate the thermodynamics of transport in mesoscopic conductors that are coupled to external reservoirs and may be driven by oscillating electromagnetic fields. We are especially interested in the interplay between dissipation, quantum and thermal fluctuations and collective effects such as Pauli blocking.


Our broader goal is to help providing the conceptual basis for new nano-devices that are driven by electric or heat currents. In particular, we aim to find new strategies to measure and improve the performance of such devices. Potential applications include quantum thermoelectric generators and refrigerators for waste-heat recovery and cooling and quantum motors, which may be used to propel future nano-machines.




  • E. Potanina, C. Flindt, M. Moskalets, K. Brandner  Thermodynamic bounds on coherent transport in periodically driven conductors, Phys. Rev. X 11 021013.

  • P. Menczel, E. Loisa, K. Brandner, C. Flindt  Thermodynamic uncertainty relations for coherently driven open quantum systems, J. Phys. A: Math. Theor. 54 314002.


  • F. Carollo, K. Brandner, I. Lesanovsky Nonequilibrium Many-Body Quantum Engine Driven by Time-Translation Symmetry Breaking, Phys. Rev. Lett. 125 240602.

  • P. Menczel, C. Flindt, K. Brandner Quantum jump approach to microscopic heat engines,
    Phys. Rev. Research 2 033449.

  • K. Brandner Coherent Transport in Periodically Driven Mesoscopic Conductors: From Scattering Amplitudes to Quantum Thermodynamics, Z. Naturforsch. 75 483.

  • P. Menczel, C. Flindt, K. Brandner Thermodynamics of cyclic quantum amplifiers, Phys. Rev. A 101 052106.

  • F. Carollo, F. M. Gambetta, K. Brandner, J. P. Garrahan, I. Lesanovsky Nonequilibrium Quantum Many-Body Rydberg Atom Engine, Phys. Rev. Lett. 124 170602.

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










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