Abstract
Recent experimental breakthroughs produced the first nano heat engines that have the potential to harness quantum resources. An instrumental question is how their performance measures up against the efficiency of classical engines. For single ion engines undergoing quantum Otto cycles it has been found that the efficiency at maximal power is given by the Curzon–Ahlborn efficiency. This is rather remarkable as the Curzon–Alhbron efficiency was originally derived for endoreversible Carnot cycles. Here, we analyze two examples of endoreversible Otto engines within the same conceptual framework as Curzon and Ahlborn’s original treatment. We find that for endoreversible Otto cycles in classical harmonic oscillators the efficiency at maximal power is, indeed, given by the Curzon–Ahlborn efficiency. However, we also find that the efficiency of Otto engines made of quantum harmonic oscillators is significantly larger.
Highlights
Recent experimental breakthroughs produced the first nano heat engines that have the potential to harness quantum resources
For cycles involving only unitary strokes [7,8] the assumption of local equilibrium is almost never justified, and it becomes even more remarkable that at maximal power output a quantum Otto cycle in a parametric, harmonic oscillator operates with the Curzon–Ahlborn efficiency [7,8]
We find that in this case the efficiency is larger than ηCA (1), which demonstrates that the Curzon–Ahlborn efficiency is not universal at maximal power
Summary
It is a standard exercise of thermodynamics to compute the efficiency of engines, i.e., to determine the relative work output for devices undergoing cyclic transformations on the thermodynamic manifold [1]. For cycles involving only unitary strokes [7,8] the assumption of local equilibrium is almost never justified, and it becomes even more remarkable that at maximal power output a quantum Otto cycle in a parametric, harmonic oscillator operates with the Curzon–Ahlborn efficiency [7,8]. The purpose of the present work is to revisit these longstanding questions and study the endoreversible Otto cycle in a conceptually simple and pedagogical approach similar to Curzon and Ahlborn’s original treatment [2]. To this end, we compute the efficiency at maximal power for two examples of endoreversible Otto engines. E.g., neither the full quantum dynamics [6] nor the linear response problem [10] have to be solved
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