This talk will cover recent advances in the field of Quantum Thermodynamics, an emerging field that aims to uncover the thermodynamic laws at the nanoscale [1]. I will begin with explaining a (classical) nanoscale thermodynamic experiment with optically trapped nanospheres that undergo Brownian motion in air [2]. These spheres experience a non-equilibrium situation due to heating from the trapping laser. By using a suitable two-bath model to analyse the data, one can infer the surface temperature of the trapped spheres and also observe temperature gradients across the nanospheres. I will then move on to theoretical results concerning thermodynamic work in the quantum regime, i.e. can a different amount of work be extracted from a quantum system than from a classical system? To solve this we set up a quantum thermodynamic process that removes quantum information in analogy to Landauerâ€™s erasure of classical information. The thermodynamic analysis of such a process uncovers that work can be extracted from quantum coherences in addition to the work that can be extracted from classical non-equilibrium states [3]. Finally, I will report on a thermodynamic uncertainty relation that limits the accuracy of measuring the temperature and energy of a thermal quantum system [4]. Corrections to the standard uncertainty relation arise here because, unlike in standard thermodynamics, a small systemâ€™s interaction with its environment is not negligible. The emerging relation unites thermodynamic and quantum uncertainties for the first time.

[1] Quantum thermodynamics, S. Vinjanampathy, J. Anders, Contemporary Physics 57, 545 (2016).
[2] Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere, J. Millen, T. Deesuwan, P. Barker, J. Anders, Nature Nanotechnology 9, 425 (2014).
[3] Coherence and measurement in quantum thermodynamics, P. Kammerlander, J. Anders, Scientific Reports 6, 22174 (2016).
[4] Energy-temperature uncertainty relation in quantum thermodynamics, H. Miller, J. Anders, Nature Communications 9:2203 (2018).

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