Efficiency bounds for nonequilibrium heat engines

Mehta, Pankaj; Polkovnikov, Anatoli

doi:10.1016/J.AOP.2013.01.017

Title: Efficiency bounds for nonequilibrium heat engines

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Abstract

We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines.more »« less

Authors:: Mehta, Pankaj; Polkovnikov, Anatoli

Publication Date:: Wed May 15 00:00:00 EDT 2013

OSTI Identifier:: 22220716

Resource Type:: Journal Article

Journal Name:: Annals of Physics (New York)

Additional Journal Information:: Journal Volume: 332; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATMOSPHERES; COMBUSTION; DESIGN; DISTRIBUTION; EFFICIENCY; ENTROPY; EQUILIBRIUM; FUELS; HEAT; HEAT ENGINES; STATISTICAL MECHANICS; THERMODYNAMICS

Citation Formats


                    Mehta, Pankaj, and Polkovnikov, Anatoli. Efficiency bounds for nonequilibrium heat engines.  United States: N. p., 2013. 
        Web.  doi:10.1016/J.AOP.2013.01.017.

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                    Mehta, Pankaj, & Polkovnikov, Anatoli. Efficiency bounds for nonequilibrium heat engines.  United States.  https://doi.org/10.1016/J.AOP.2013.01.017

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                    Mehta, Pankaj, and Polkovnikov, Anatoli. 2013.  
        "Efficiency bounds for nonequilibrium heat engines".  United States.  https://doi.org/10.1016/J.AOP.2013.01.017.

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@article{osti_22220716,

  title        = {Efficiency bounds for nonequilibrium heat engines},

  author       = {Mehta, Pankaj and Polkovnikov, Anatoli},

  abstractNote = {We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples. -- Highlights: ► Derived efficiency bounds for heat engines working with a single reservoir. ► Analyzed both ergodic and non-ergodic engines. ► Showed that non-ergodic engines can be more efficient. ► Extended fundamental thermodynamic relation to arbitrary nonequilibrium processes.},

  doi          = {10.1016/J.AOP.2013.01.017},

  url          = {https://www.osti.gov/biblio/22220716},
  journal      = {Annals of Physics (New York)},

  issn         = {0003-4916},

  number       = ,

  volume       = 332,

  place        = {United States},

  year         = {Wed May 15 00:00:00 EDT 2013},

  month        = {Wed May 15 00:00:00 EDT 2013}

}

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