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Journal of Modern Physics

Quantum Heat Engines; Multiple-State 1D Box System

Eny Latifah, Agus Purwanto

Published Jan 1, 2013• 29 citations
Publisher

Abstract

We evaluate quantum Otto, Diesel and Brayton cycles employing multiple-state 1D box system instead of ideal gas filled cylinder. The work and heat are extracted using the change in the expectation of Hamiltonian of the system which leads to the first law of thermodynamics to quantum system. The first law makes available to redefine the force which is in fact not well defined in a quantum mechanical system and then it is applied to define the quantum version of thermodynamic processes, i.e. isobaric, isovolume and adiabatic. As the results, the efficiency of quantum Otto engine depends only on the compression ratio and will be higher than the efficiency of quantum Diesel which can decrease by the widening of expansion under isobaric process. The efficiency of quantum Brayton engine may reach maximum on certain combination between the wide of box under isobaric expansion and compression, under certain conditions. The amount of levels participated in the quantum heat engine system will potentially reduce the performance of the quantum heat cycles consisting isobaric process, but it can be resisted using isobaric process controller.

DOI
10.4236/jmp.2013.48146

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We evaluate quantum Otto, Diesel and Brayton cycles employing multiple-state 1D box system instead of ideal gas filled cylinder. The work and heat are extracted using the change in the expectation of Hamiltonian of the system which leads to the first law of thermodynamics to quantum system. The first law makes available to redefine the force which is in fact not well defined in a quantum mechanical system and then it is applied to define the quantum version of thermodynamic processes, i.e. isobaric, isovolume and adiabatic. As the results, the efficiency of quantum Otto engine depends only on the compression ratio and will be higher than the efficiency of quantum Diesel which can decrease by the widening of expansion under isobaric process. The efficiency of quantum Brayton engine may reach maximum on certain combination between the wide of box under isobaric expansion and compression, under certain conditions. The amount of levels participated in the quantum heat engine system will potentially reduce the performance of the quantum heat cycles consisting isobaric process, but it can be resisted using isobaric process controller.
We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.
In this work, a quantum Otto engine (QOE) based on a multiple-state single fermion particle trapped in an one-dimensional potential well has been studied. In this study, we used an analogical model completed with the first law of thermodynamics for the quantum system. The system satisfied the relativistic Hamiltonian, especially Dirac Hamiltonian. The engine consisted of the quantum isochoric and isentropic processes to form an Otto Cycle. The heat input and output were transferred under isochoric processes. As a result, the higher the number of energies was arranged, the lower the efficiency the system has. However, we could increase the efficiency of QOE by controlling the compression ratio. In addition, we also obtained the correspondence of the efficiency ultra-relativistic limits QOE and non-relativistic limits one.
A quantum dual-engine is a machine that applies a dual cycle in a quantum system. This machine is a quantum analogy to the classical dual-engine consisting of a combination of classical Otto engine and classical Diesel engine. By analogizing a particle in a one-dimensional infinite potential well as a gas in a piston-cylinder, quantum thermodynamic processes in a dual cycle can be explained from the analogies of classical processes such as adiabatic, isochoric, and isobar. This research examines the value of thermal efficiency and other aspects of the quantum dual-engine with the study of literature. The results of the research show that the thermal efficiency of the quantum dual-engine has similarities with the classical dual-engine. Under the same mechanical ratios condition, the thermal efficiency of a quantum dual-engine has a higher value than the thermal efficiency of its classical engines.
We explore the quantum version of Brayton cycle with a composite system as the working substance. The actual Brayton cycle consists of two adiabatic and two isobaric processes. Two pressures can be defined in our isobaric process, one corresponds to the external magnetic field (characterized by FxF_xFx​) exerted on the system, while the other corresponds to the coupling constant between the subsystems (characterized by FyF_yFy​). As a consequence, we can define two types of quantum Brayton cycle for the composite system. We find that the subsystem experiences a quantum Brayton cycle in one quantum Brayton cycle (characterized by FxF_xFx​), whereas the subsystem's cycle is of quantum Otto in another Brayton cycle (characterized by FyF_yFy​). The efficiency for the composite system equals to that for the subsystem in both cases, but the work done by the total system are usually larger than the sum of work done by the two subsystems. The other interesting finding is that for the cycle characterized by FyF_yFy​, the subsystem can be a refrigerator while the total system is a heat engine. The result in the paper can be generalized to a quantum Brayton cycle with a general coupled system as the working substance.
A quantum Brayton engine using a massless Boson trapped in a one-dimensional potential well as a working substance has been constructed to be studied. We used a modified analogical model by the first law of thermodynamics for a quantum system implementation. The system was built with Klein Gordon equation, relativistic quantum mechanics Hamiltonian, without the mass term of the Hamiltonian and it was trapped in a one-dimensional potential well. Then, it underwent the quantum ideal Brayton cycle process. The quantum Brayton process consisted of adiabatic compression, isobaric expansion, adiabatic expansion, and isobaric compression processes. This relativistic quantum mechanics Brayton engine has found that the efficiency formulation was similar to the classical one. This study obtained the conformity results between the quantum relativistic and classical Brayton engines. By this cycle process, we also invented that the ratio of heat capacity under constant pressure and volume of the system was 2. It could indicate that the efficiency of quantum relativistic Brayton engine is higher than the classical one.