Abstract
How much work can be extracted from a heat bath using a thermal machine? The study of this question has a very long history in statistical physics in the weak-coupling limit, when applied to macroscopic systems. However, the assumption that thermal heat baths remain uncorrelated with associated physical systems is less reasonable on the nano-scale and in the quantum setting. In this work, we establish a framework of work extraction in the presence of quantum correlations. We show in a mathematically rigorous and quantitative fashion that quantum correlations and entanglement emerge as limitations to work extraction compared to what would be allowed by the second law of thermodynamics. At the heart of the approach are operations that capture the naturally non-equilibrium dynamics encountered when putting physical systems into contact with each other. We discuss various limits that relate to known results and put our work into the context of approaches to finite-time quantum thermodynamics.
Highlights
IntroductionThe theory of thermodynamics originates from the study of thermal machines in the early industrial age, when it was of utmost importance to find out what rates of work extraction could
In this work we have introduced a framework to study work extraction in thermal machines
System–bath entanglement seriously limits the amount of work extractable and induces irreversibility in the process, which in turn prevents one from saturating the second law of thermodynamics
Summary
The theory of thermodynamics originates from the study of thermal machines in the early industrial age, when it was of utmost importance to find out what rates of work extraction could. S equilibrates to the usual Gibbs ensemble Note that this notion of weak coupling can in general differ from the one sometimes used in the study of open quantum systems leading to Markovian dynamics of the sub-system S [3, 10]. The precise conditions on the coupling so that (1) is fulfilled have been recently tackled in the quantum setting: the strength of the coupling Hamiltonian V—measured in an adequate norm—has to be negligible in comparison with the intensive thermal energy scale β−1 [11] This formalizes the usual derivation of the canonical ensemble from the micro-canonical one in classical statistical mechanics where the coupling energy is neglected. Our results are completely general in the sense that they do not make use of any specific model for the description of the system or bath
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