Abstract
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 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-, 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 , 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.
Highlights
Optimal control of physical and chemical systems, and of the processes taking place in such systems, has been a major goal since the beginning of scientific investigations [1,2]
We have presented three thermodynamic cycles for a hydrogen atom-like system in (κ, T ) space, where κ allows us to control the electronic energy levels of the system: iso-κ-isothermal, iso-κ-adiabatic, and adiabatic-isothermal
We have written down expressions for heat and work along the legs of these cycles and derived conditions that yield optimal ways to run through the cycles in finite time such that the entropy production or the excess heat production is minimal
Summary
Optimal control of physical and chemical systems, and of the processes taking place in such systems, has been a major goal since the beginning of scientific investigations [1,2]. A second aspect of optimal control based on the laws of physics is to reduce the engine under consideration to the most elementary physical systems that are stripped of all weaknesses and complications which are associated with the macroscopic aspects of the experimental apparatus employed in their realization, resulting in the creation and investigation of molecular machines [12] This involves reducing the size of the system in the sense that we are dealing with a macroscopic system as a (non-interacting) ensemble of elementary but microscopic systems. States-based engine, not with a standard thermal atom movement-based engine as studied, e.g., in [13]
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