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Resource Theory of Quantum Thermodynamics: Thermal Operations and Second Laws

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Thermodynamics in the Quantum Regime

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 195))

Abstract

Resource theories are a generic approach used to manage any valuable resource, such as entanglement, purity, and asymmetry. Such frameworks are characterized by two main elements: a set of predefined (free) operations and states, that one assumes to be easily obtained at no cost. Given these ground rules, one can ask: what is achievable by using such free operations and states? This usually results in a set of state transition conditions, that tell us if a particular state \( \rho \) may evolve into another state \( \rho ' \) via the usage of free operations and states. We shall see in this chapter that thermal interactions can be modelled as a resource theory. The state transition conditions arising out of such a framework, are then referred to as “second laws”. We shall also see how such state transition conditions recover classical thermodynamics in the i.i.d. limit. Finally, we discuss how these laws are applied to study fundamental limitations to the performance of quantum heat engines.

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Notes

  1. 1.

    Any state which is not a free state is then called a resource state.

  2. 2.

    Up to an arbitrarily good approximation to the final state \(\rho _S'\) for fixed dimensional \(\mathcal {H}_S\), in operator norm.

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Acknowledgements

N.N. acknowledges funding from the Alexander von Humboldt foundation. M.W. acknowledges the Swiss National Science Foundation (SNSF) via the NCCR QSIT. M.W. would like to acknowledge the COST MP1209 network “Thermodynamics in the quantum regime”, to which he was a member and from which part of the research reviewed in this chapter was made possible.

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Authors and Affiliations

  1. Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany

    Nelly Huei Ying Ng

  2. Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Str. 27, 8093, Zürich, Switzerland

    Mischa Prebin Woods

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  1. Nelly Huei Ying Ng
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Correspondence to Mischa Prebin Woods .

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Editors and Affiliations

  1. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Felix Binder

  2. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    Luis A. Correa

  3. ICFO: Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels, Spain

    Christian Gogolin

  4. CEMPS, Physics and Astronomy, University of Exeter, Exeter, UK

    Janet Anders

  5. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    Gerardo Adesso

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Ng, N.H.Y., Woods, M.P. (2018). Resource Theory of Quantum Thermodynamics: Thermal Operations and Second Laws. In: Binder, F., Correa, L., Gogolin, C., Anders, J., Adesso, G. (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol 195. Springer, Cham. https://doi.org/10.1007/978-3-319-99046-0_26

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