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Open AccessArticle

Optimal Control of Hydrogen Atom-Like Systems as Thermodynamic Engines in Finite Time

Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
Entropy 2020, 22(10), 1066; https://doi.org/10.3390/e22101066
Received: 27 August 2020 / Revised: 17 September 2020 / Accepted: 19 September 2020 / Published: 23 September 2020
(This article belongs to the Special Issue Finite-Time Thermodynamics)
Nano-size machines are moving from only being topics of basic research to becoming elements in the toolbox of engineers, and thus the issue of optimally controlling their work cycles becomes important. Here, we investigate hydrogen atom-like systems as working fluids in thermodynamic engines and their optimal control in minimizing entropy or excess heat production in finite-time processes. The electronic properties of the hydrogen atom-like system are controlled by a parameter κ reflecting changes in, e.g., the effective dielectric constant of the medium where the system is embedded. Several thermodynamic cycles consisting of combinations of iso-κ, isothermal, and adiabatic branches are studied, and a possible a-thermal cycle is discussed. Solving the optimal control problem, we show that the minimal thermodynamic length criterion of optimality for finite-time processes also applies to these cycles for general statistical mechanical systems that can be controlled by a parameter κ, and we derive an appropriate metric in probability distribution space. We show how the general formulas we have obtained for the thermodynamic length are simplified for the case of the hydrogen atom-like system, and compute the optimal distribution of process times for a two-state approximation of the hydrogen atom-like system. View Full-Text
Keywords: optimal control; thermodynamic cycles; finite-time thermodynamics; thermodynamic length; hydrogen atom; nano-size engines; a-thermal cycle optimal control; thermodynamic cycles; finite-time thermodynamics; thermodynamic length; hydrogen atom; nano-size engines; a-thermal cycle
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Schön, J.C. Optimal Control of Hydrogen Atom-Like Systems as Thermodynamic Engines in Finite Time. Entropy 2020, 22, 1066.

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