## Quantum Thermodynamics & Quantum Information theory

#### Three-dimensional quantum spin dynamics equation

Spin precession in magnetic materials is commonly modelled with the classical phenomenological Landau-Lifshitz-Gilbert (LLG) equation. Recent work has addressed shortcomings, however no quantum thermodynamically consistent framework has been compared to the predictions of the standard LLG equa- tion. Based on a quantized spin+environment Hamiltonian, we here derive a general three-dimensional quantum spin dynamics equation that consistently accounts for effects arising from memory, coloured noise and quantum statistics. We further propose resonant Lorentzian couplings as a tool for the system- atic comparison of spin dynamics in non-LLG-like and LLG-like regimes. We demonstrate characteristic flattening of the magnetization curve of a single classical spin at low temperatures, caused by quantum noise fluctuations that persist even at zero temperature. For dynamics with appreciable memory times our numerical results show a decay to steady state that is much quicker than with the memory-free LLG equation. The presented model provides a powerful tool to explore general three-dimensional dissipation in quantum thermodynamics.

#### Qualitative quantum rate model for enzyme catalysed reactions

We build a qualitative quantum rate model with few free parameters that describes the transfer rates of hydrogen and deuterium in transfer reactions catalysed by enzymes, such as soybean lipoxygenase (SLO). The enzyme’s impact on the dynamics is modelled by an additional energetic term, an oscillatory contribution known as “gating.” By varying two key parameters, the gating frequency and the mean donor-acceptor separation, the model is able to reproduce the experimentally measured KIE data for SLO wild-type and a variety of SLO mutants over the experimentally accessible temperature range. While SLO-specific constants have been considered here, it is possible to adapt these for other enzymes.

#### A quantum Szilard engine without heat

Szilard’s engine has played an important role in establishing the link between information theory and thermodynamics. Whether in the classical or quantum regime, the source of work in this engine is heat drawn from a thermal reservoir. Recent research, however, has suggested the possibility of engines that, in lieu of a thermal reservoir, draw power directly from measurements. Here, we describe a general quantum Szilard engine, and conclude that if it is to draw work from projective measurements, its performance will be subject to certain restrictions. This observation is a first-step towards developing “second-law-like” relations for measurement-assisted feedback control beyond thermality.

#### Fluctuating work in the quantum histories framework

In classical statistical physics “work” is assigned with individual experiments, each characterised by a trajectory in phase space. Extending this concept to the quantum regime has been a cause of debate because of the lack of trajectories in quantum physics. One widely used solution is to measure the energy at the beginning and end of a process, and define work as the difference. However, due to the invasive nature of measurement the resulting work probability distribution does not actually describe the work statistics of the same system when it is not measured.

Using the quantum histories framework to construct trajectories we here show how the characterisation of “work” of the unmeasured dynamics is possible. We find that the unmeasured work “probability” distribution can have negative “probabilities” highlighting distinctly non-classical features of quantum work. Of course, for classical systems the work of a system when it is measured and or not is identical, reflecting the fact that only in the quantum world it matters whether “one looks at the moon or not”, as Einstein and Bohr debated.

#### Enhanced Energy Transfer to an Optomechanical Piston from Indistinguishable Photons

Thought experiments involving gases and pistons, such as Maxwell’s demon and Gibbs’ mixing, are central to our understanding of thermodynamics. Here, we present a quantum thermodynamic thought experiment in which the energy transfer from two photonic gases to a piston membrane grows quadratically with the number of photons for indistinguishable gases, while it grows linearly for distinguishable gases. This signature of bosonic bunching may be observed in optomechanical experiments, highlighting the potential of these systems for the realization of thermodynamic thought experiments in the quantum realm.

#### Observing a Maxwell demon at work

In apparent contradiction to the laws of thermodynamics, Maxwell’s demon is able to cyclically extract work from a system in contact with a thermal bath exploiting the information about its microstate. The resolution of this paradox required the insight that an intimate relationship exists between information and thermodynamics. We realize a Maxwell demon experiment that tracks the state of each constituent both in the classical and quantum regimes. The demon is a microwave cavity that encodes quantum information about a superconducting qubit and converts information into work by powering up a propagating microwave pulse by stimulated emission. Thanks to the high level of control of superconducting circuits, we directly measure the extracted work and quantify the entropy remaining in the demon’s memory. This experiment provides an enlightening illustration of the interplay of thermodynamics with quantum information.

#### Entropy production in the presence of strong interactions

Standard thermodynamics rests on the assumption of systems being only weakly coupled to their environment. However, with experiments entering the strong coupling regime the extension of thermodynamic concepts, such as entropy production, to this limit is now of practical importance. We here show that the concept of entropy production can be carried over to the strong coupling regime, where it measures time-asymmetry and deviations from (a generalised class of) equilibrium states, in analogy to weakly coupled thermodynamics. The resulting detailed entropy fluctuation relations pave the way to optimising the performance of small scale thermal machines where strong interactions cannot be neglected.

#### Work value of quantum Coherences

#### Non-equilibrium temperatures of light-levitated nanospheres

Einstein realised that the fluctuations of a Brownian particle can be used to ascertain properties of its environment. For nanospheres levitated by a laser in a dilute gas we develop a theoretical model that allows one to infer the surface temperature of the spheres, as well as the temperature of the gas in the vicinity of the sphere. We demonstrate this method experimentally and observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and provides a means for testing non-equilibrium thermodynamics.