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Physical Review Letters

Extracting Work from a Single Thermal Bath via Quantum Negentropy

Marlan O. Scully

Published Nov 12, 2001• 181 citations
Publisher

Abstract

Classical heat engines produce work by operating between a high temperature energy source and a low temperature entropy sink. The present quantum heat engine has no cooler reservoir acting as a sink of entropy but has instead an internal reservoir of negentropy which allows extraction of work from one thermal bath. The process is attended by constantly increasing entropy and does not violate the second law of thermodynamics.

DOI
10.1103/physrevlett.87.220601

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Classical heat engines produce work by operating between a high temperature energy source and a low temperature entropy sink. The present quantum heat engine has no cooler reservoir acting as a sink of entropy but has instead an internal reservoir of negentropy which allows extraction of work from one thermal bath. The process is attended by constantly increasing entropy and does not violate the second law of thermodynamics.
According to the Second Law of Thermodynamics, a heat engine requires two heat baths to operate-a warm source of heat and a cooler dump for waste heat. In apparent violation of this law, Scully et al. propose a heat engine that uses quantum coherence to extract work from a single, warm gas. In his Perspective, Linke explains that the Second Law is not violated, because the power extracted from the bath is smaller than that required to achieve coherence. By combining quantum mechanics with traditional heat engines, the efficiencies of various kinds of motors could be enhanced.
Conventional heat engines convert thermal energy into mechanical work by using a working medium such as steam or gas that operates between a hot and a cold reservoir. The medium absorbs heat from the hot reservoir, produces work, then releases some heat to the cold reservoir and returns to the initial state. With the advancement of quantum technologies, researchers strive to understand whether quantum media, such as atoms, spins, superconducting circuits and semiconductor quantum dots, can be used in quantum counterparts of the classical heat engines. After a recap of the basics of classical heat engines, this review explores the theoretical foundations and advancements of quantum heat engines, focusing on the proposed two- and multilevel systems used as the working medium for the quantum Otto cycle, which is the ideal thermodynamic cycle that describes the operation of a spark-ignition internal combustion engine. The review compares the efficiency and the work extraction of these systems, discussing their performance in the high- and low-temperature limits. Alternative cycles and engines are also presented to establish the adaptability of the working media when operating under different processes and non-equilibrium conditions. In conclusion, the review offers possible applications and future developments of quantum heat engines.
We present here a quantum Carnot engine in which the atoms in the heat bath are given a small bit of quantum coherence. The induced quantum coherence becomes vanishingly small in the high-temperature limit at which we operate and the heat bath is essentially thermal. However, the phase phi, associated with the atomic coherence, provides a new control parameter that can be varied to increase the temperature of the radiation field and to extract work from a single heat bath. The deep physics behind the second law of thermodynamics is not violated; nevertheless, the quantum Carnot engine has certain features that are not possible in a classical engine.
With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's demon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.
t is possible to extract work from a quantum-mechanical system whose dynamics is governed by a time-dependent cyclic Hamiltonian. An energy bath is required to operate such a quantum engine in place of the heat bath used to run a conventional classical thermodynamic heat engine. The effect of the energy bath is to maintain the expectation value of the system Hamiltonian during an isoenergetic process. It is shown that the existence of such a bath leads to equilibrium quantum states that maximise the von Neumann entropy. Quantum analogues of certain thermodynamic relations are obtained that allow one to define the temperature of the energy bath.
It is possible to extract work from a quantum–mechanical system whose dynamics is governed by a time–dependent cyclic Hamiltonian. An energy bath is required to operate such a quantum engine in place of the heat bath used to run a conventional classical thermodynamic heat engine. The effect of the energy bath is to maintain the expectation value of the system Hamiltonian during an isoenergetic process. It is shown that the existence of such a bath leads to equilibrium quantum states that maximize the von Neumann entropy. Quantum analogues of certain thermodynamic relations are obtained that allow one to define the temperature of the energy bath.