Abstract
The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes --- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced ``control-marginal state" --- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.
Highlights
Microscopic thermal heat engine has been recently realised in the lab with a trapped single calcium ion operating as a working body [1], as well as in superconducting circuits [2], nitrogen vacancy centers in diamond [3], and electromechanical [4] settings
With local terms corresponding to the subsystems. In this setting we introduce the general thermodynamic framework characterized by five defining properties: (A1) Energy conserving stroke operations; (A2) Heat baths in equilibrium; (A3) Explicit battery given by the weight; (A4) Two-dimensional working body; (A5) Cyclicity of the heat engine
The main achievement of this work is the establishment of new fundamental limits for the performance of quantum heat engines, which to Carnot result are independent of microscopic details of engine dynamics
Summary
Our model of a heat engine consists of four main parts. Hot bath H, which plays the role of the energy source, cold bath C, used as a sink for the entropy (or passive energy, see further in the article), battery B, which plays a role of an energy storage, and a working body S, which steers the flow of the energy between the other subsystems (Fig. 1). (A1) Energy conserving stroke operations; (A2) Heat baths in equilibrium; (A3) Explicit battery given by the weight; (A4) Two-dimensional working body; (A5) Cyclicity of the heat engine. In contrast to the approaches where particular dynamics leading to the unitary USB is proposed explicitly, the ideal weight is defined by imposing a symmetry which it has to obey This is a translational invariance symmetry, which alludes to the intuition that change of the energy should not depend on how much energy is already stored in the battery. According to the strict law of energy conservation (3), it is important to stress that in this framework the total free Hamiltonian H0 (1) of the engine remains constant during the whole protocol This is essentially different from non-autonomous approaches with modulated energy levels of a working body by an external control [40].
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