Quantum engine efficiency bound beyond the second law of thermodynamics (original) (raw)

Quantum thermodynamic cycles and quantum heat engines

Physical Review E, 2007

In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwell's demon in quantum thermodynamic cycles. We find that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine.

Quantum heat engines, the second law and Maxwell's daemon

The European Physical Journal D, 2006

We introduce a class of quantum heat engines which consists of two-energy-eigenstate systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and energy exchanges with heat baths, respectively, at different stages of a cycle. Armed with this class of heat engines and some interpretation of heat transferred and work performed at the quantum level, we are able to clarify some important aspects of the second law of thermodynamics. In particular, it is not sufficient to have the heat source hotter than the sink, but there must be a minimum temperature difference between the hotter source and the cooler sink before any work can be extracted through the engines. The size of this minimum temperature difference is dictated by that of the energy gaps of the quantum engines involved. Our new quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. Inspired and motivated by the Rabi oscillations, we further introduce some modifications to the quantum heat engines with single-mode cavities in order to, while respecting the second law, extract more work from the heat baths than is otherwise possible in thermal equilibria. Some of the results above are also generalisable to quantum heat engines of an infinite number of energy levels including 1-D simple harmonic oscillators and 1-D infinite square wells.

Work extremum principle: Structure and function of quantum heat engines

Physical Review E, 2008

We consider a class of quantum heat engines consisting of two subsystems interacting with a work-source and coupled to two separate baths at different temperatures Th>Tc . The purpose of the engine is to extract work due to the temperature difference. Its dynamics is not restricted to the near equilibrium regime. The engine structure is determined by maximizing the extracted work under various constraints. When this maximization is carried out at finite power, the engine dynamics is described by well-defined temperatures and satisfies the local version of the second law. In addition, its efficiency is bounded from below by the Curzon-Ahlborn value 1-Tc/Th and from above by the Carnot value 1-(Tc/Th) . The latter is reached—at finite power—for a macroscopic engine, while the former is achieved in the equilibrium limit Th→Tc . The efficiency that maximizes the power is strictly larger than the Curzon-Ahloborn value. When the work is maximized at a zero power, even a small (few-level) engine extracts work right at the Carnot efficiency.

Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine

Entropy

Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin of irreversibility, originating from heat transport, quantum friction, and thermalization in the presence of external driving. We construct various finite-time engine cycles that are based on the Otto and Carnot templates. Our analysis highlights the role of coherence and the quantum origin of entropy production.

Quantum thermodynamics and quantum coherence engines

TURKISH JOURNAL OF PHYSICS

Advantages of quantum effects in several technologies, such as computation and communication, have already been well appreciated, and some devices, such as quantum computers and communication links, exhibiting superiority to their classical counterparts have been demonstrated. The close relationship between information and energy motivates us to explore if similar quantum benefits can be found in energy technologies. Investigation of performance limits for a broader class of information-energy machines is the subject of the rapidly emerging field of quantum thermodynamics. Extension of classical thermodynamical laws to the quantum realm is far from trivial. This short review presents some of the recent efforts in this fundamental direction and focuses on quantum heat engines and their efficiency bounds when harnessing energy from non-thermal resources, specifically those containing quantum coherence and correlations.

Irreversible performance of a quantum harmonic heat engine

New Journal of Physics, 2006

The unavoidable irreversible loss of power in a heat engine is found to be of quantum origin. Following thermodynamic tradition, a model quantum heat engine operating in an Otto cycle is analysed, where the working medium is composed of an ensemble of harmonic oscillators and changes in volume correspond to changes in the curvature of the potential well. Equations of motion for quantum observables are derived for the complete cycle of operation. These observables are sufficient to determine the state of the system and with it all thermodynamical variables. Once the external controls are set, the engine settles to a limit cycle. Conditions for optimal work, power and entropy production are derived. At high temperatures and quasistatic operating conditions, the efficiency at maximum power coincides with the endoreversible result η q = 1 − √ T c /T h . The optimal compression ratio varies from C = √ T h /T c in the quasistatic limit where the irreversibility is dominated by heat conductance to C = (T h /T c ) 1/4 in the sudden limit when the irreversibility is dominated by friction. When the engine deviates from adiabatic conditions, the performance is subject to friction. The origin of this friction can be traced to the noncommutability of the kinetic and potential energy of the working medium.

Introduction to Quantum Thermodynamics: History and Prospects

Thermodynamics in the Quantum Regime, 2018

Quantum Thermodynamics is a continuous dialogue between two independent theories: Thermodynamics and Quantum Mechanics. Whenever the two theories have addressed the same phenomena new insight has emerged. We follow the dialogue from equilibrium Quantum Thermodynamics and the notion of entropy and entropy inequalities which are the base of the II-law. Dynamical considerations lead to nonequilibrium thermodynamics of quantum Open Systems. The central part played by completely positive maps is discussed leading to the Gorini-Kossakowski-Lindblad-Sudarshan "GKLS" equation. We address the connection to thermodynamics through the system-bath weak-coupling-limit WCL leading to dynamical versions of the I-law. The dialogue has developed through the analysis of quantum engines and refrigerators. Reciprocating and continuous engines are discussed. The autonomous quantum absorption refrigerator is employed to illustrate the III-law. Finally, we describe some open questions and perspectives.

The thermodynamic cost of quantum operations

The amount of heat generated by computers is rapidly becoming one of the main problems for developing new generations of information technology. The thermodynamics of computation sets the ultimate physical bounds on heat generation. A lower bound is set by the Landauer Limit, at which computation becomes thermodynamically reversible. For classical computation there is no physical principle which prevents this limit being reached, and approaches to it are already being experimentally tested. In this paper we show that for quantum computation there is an unavoidable excess heat generation that renders it inherently thermodynamically irreversible. The Landauer Limit cannot, in general, be reached by quantum computers. We show the existence of a lower bound to the heat generated by quantum computing that exceeds that given by the Landauer Limit, give the special conditions where this excess cost may be avoided, and show how classical computing falls within these special conditions.

The second laws of quantum thermodynamics

Proceedings of the National Academy of Sciences of the United States of America, 2015

The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparen...