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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Thermodynamics and Field Theory

MP 3.1: Hauptvortrag

Dienstag, 20. März 2018, 16:30–17:15, Z6 - SR 1.012

Operational meaning of entropy and free energy without the thermodynamic limit — •Markus P. Müller — Institut für Quantenoptik und Quanteninformation, Boltzmanngasse 3, 1090 Wien, Österreich

Thermodynamics at the nanoscale is known to behave very differently from the familiar regime of the thermodynamic limit. It has been shown that quantum fluctuations lead to severe restrictions on work extraction and state transformations: e.g. the constraint of Helmholtz free energy decrease is replaced by an infinite sequence of ``second laws'' (cf. Brandao et al., PNAS 112, 2015). In contrast, here we show a surprising positive feature of small-scale thermodynamics which is absent in the standard regime: microscopic thermal machines can tame fluctuations by building up correlations with the particles on which they act. That is, these machines can increase their efficiency via clever ``correlation engineering''. We prove that they can thus extract or invest the Helmholtz free energy difference exactly and basically without any fluctuations, which restores the original form of the second law in the nano regime.

This result rests on new theorems on majorization of probability distributions which can also be applied in quantum information theory beyond thermodynamics: they allow us to give operational `single-shot' interpretations of the von Neumannn entropy and the mutual information, without considering a large number of copies of a quantum state.

Based partially on arXiv:1707.03451.