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Work cost of thermal operations in quantum thermodynamics

  • Joseph M. Renes
Regular Article
Part of the following topical collections:
  1. Focus Point on Quantum information and complexity

Abstract.

Adopting a resource theory framework of thermodynamics for quantum and nano systems pioneered by Janzing et al. (Int. J. Th. Phys. 39, 2717 (2000)), we formulate the cost in the useful work of transforming one resource state into another as a linear program of convex optimization. This approach is based on the characterization of thermal quasiorder given by Janzing et al. and later by Horodecki and Oppenheim (Nat. Comm. 4, 2059 (2013)). Both characterizations are related to an extended version of majorization studied by Ruch, Schranner and Seligman under the name mixing distance (J. Chem. Phys. 69, 386 (1978)).

Keywords

Convex Optimization Resource State Lorenz Curve Gibbs State Resource Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Elliott H. Lieb, Jakob Yngvason, Phys. Rep. 310, 1 (1999)CrossRefzbMATHADSGoogle Scholar
  2. 2.
    D. Janzing, P. Wocjan, R. Zeier, R. Geiss, Th. Beth, Int. J. Theor. Phys. 39, 2717 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Fernando G.S.L. Brando, Micha Horodecki, Jonathan Oppenheim, Joseph M. Renes, Robert W. Spekkens, Phys. Rev. Lett. 111, 250404 (2013)CrossRefADSGoogle Scholar
  4. 4.
    Micha Horodecki, Jonathan Oppenheim, Nat. Commun. 4, 2059 (2013)Google Scholar
  5. 5.
    Ernst Ruch, Rudolf Schranner, Thomas H. Seligman, J. Chem. Phys. 69, 386 (1978)CrossRefADSGoogle Scholar
  6. 6.
    Dario Egloff, Oscar C.O. Dahlsten, Renato Renner, Vlatko Vedral, arXiv:1207.0434 (2012)
  7. 7.
    R. Landauer, IBM J. Res. Dev. 5, 183 (1961)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Arthur F. Veinott, Manag. Sci. 17, 547 (1971)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Ernst Ruch, Alden Mead, Theor. Chim. Acta 41, 95 (1976)CrossRefGoogle Scholar
  10. 10.
    Albert W. Marshall, Ingram Olkin, Barry C. Arnold, Inequalities: Theory of Majorization and Its Applications, 2nd edition (Springer, 2009)Google Scholar
  11. 11.
    Imre Csiszr, Magyar. Tud. Akad. Mat. Kutato Int. Kozl 8, 85 (1963)MathSciNetGoogle Scholar
  12. 12.
    Tetsuzo Morimoto, J. Phys. Soc. Jpn. 18, 328 (1963)CrossRefGoogle Scholar
  13. 13.
    S.M. Ali, S.D. Silvey, J. R. Stat. Soc. Ser. B 28, 131 (1966)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Gilad Gour, Markus P. Mller, Varun Narasimhachar, Robert W. Spekkens, Nicole Yunger Halpern, arXiv:1309.6586
  15. 15.
    Harry Joe, J. Math. Anal. Appl. 148, 287 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Alexander Barvinok, A Course in Convexity (American Mathematical Society, 2002)Google Scholar
  17. 17.
    Stephen Boyd, Lieven Vandenberghe, Convex Optimization (Cambridge University Press, 2004)Google Scholar
  18. 18.
    Philippe Faist, Frédéric Dupuis, Jonathan Oppenheim, Renato Renner, arXiv:1211.1037 (2012)

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsETH ZurichZurichSwitzerland

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