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Energetics of correlations in interacting systems

Nicolai Friis1,*, Marcus Huber2,3,4,†, and Martí Perarnau-Llobet4,‡

  • 1Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria
  • 2Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
  • 3Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
  • 4ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

  • *nicolai.friis@uibk.ac.at
  • marcus.huber@univie.ac.at
  • marti.perarnau@icfo.es

Phys. Rev. E 93, 042135 – Published 26 April, 2016

DOI: https://doi.org/10.1103/PhysRevE.93.042135

Abstract

A fundamental connection between thermodynamics and information theory arises from the fact that correlations exhibit an inherent work value. For noninteracting systems this translates to a work cost for establishing correlations. Here we investigate the relationship between work and correlations in the presence of interactions that cannot be controlled or removed. For such naturally coupled systems, which are correlated even in thermal equilibrium, we determine general strategies that can reduce the work cost of correlations, and illustrate these for a selection of exemplary physical systems.

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References (48)

  1. B. Coecke, T. Fritz, and R. W. Spekkens, A mathematical theory of resources, Inform. Comput. (2016), doi:10.1016/j.ic.2016.02.008.
  2. F. G. S. L. Brandão, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, The Resource Theory of Quantum States Out of Thermal Equilibrium, Phys. Rev. Lett. 111, 250404 (2013).
  3. M. Navascués and L. P. García-Pintos, Nonthermal Quantum Channels as a Thermodynamical Resource, Phys. Rev. Lett. 115, 010405 (2015).
  4. M. Horodecki and J. Oppenheim, (Quantumness in the context of) Resource Theories, Int. J. Mod. Phys. B 27, 1345019 (2013).
  5. C. Eltschka and J. Siewert, Quantifying entanglement resources, J. Phys. A: Math. Theor. 47, 424005 (2014).
  6. J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics, J. Phys. A: Math. Theor. 49, 143001 (2016).
  7. S. Vinjanampathy and J. Anders, Quantum thermodynamics, arXiv:1508.06099.
  8. J. Millen and A. Xuereb, Perspective on quantum thermodynamics, New J. Phys. 18, 011002 (2016).
  9. J. Oppenheim, M. Horodecki, P. Horodecki, and R. Horodecki, A Thermodynamical Approach to Quantifying Quantum Correlations, Phys. Rev. Lett. 89, 180402 (2002).
  10. W. H. Zurek, Quantum discord and Maxwell's demons, Phys. Rev. A 67, 012320 (2003).
  11. R. Alicki and M. Fannes, Extractable work from ensembles of quantum batteries. Entanglement helps, Phys. Rev. E 87, 042123 (2013).
  12. K. V. Hovhannisyan, M. Perarnau-Llobet, M. Huber, and A. Acín, Entanglement Generation is Not Necessary for Optimal Work Extraction, Phys. Rev. Lett. 111, 240401 (2013).
  13. F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantacell: Powerful charging of quantum batteries, New J. Phys. 17, 075015 (2015).
  14. H. Wilming, R. Gallego, and J. Eisert, Second law of thermodynamics under control restrictions, Phys. Rev. E 93, 042126 (2016).
  15. T. Sagawa and M. Ueda, Second Law of Thermodynamics with Discrete Quantum Feedback Control, Phys. Rev. Lett. 100, 080403 (2008).
  16. L. Del Rio, J. Åberg, R. Renner, O. Dahlsten, and V. Vedral, The thermodynamic meaning of negative entropy, Nature (London) 474, 61 (2011).
  17. K. Funo, Y. Watanabe, and M. Ueda, Thermodynamic work gain from entanglement, Phys. Rev. A 88, 052319 (2013).
  18. N. Brunner, M. Huber, N. Linden, S. Popescu, R. Silva, and P. Skrzypczyk, Entanglement enhances cooling in microscopic quantum fridges, Phys. Rev. E 89, 032115 (2014).
  19. H. C. Braga, C. C. Rulli, T. R. de Oliveira, and M. S. Sarandy, Maxwell's demon in multipartite quantum correlated system, Phys. Rev. A 90, 042338 (2014).
  20. M. Lostaglio, M. P. Müller, and M. Pastena, Stochastic Independence as a Resource in Small-Scale Thermodynamics, Phys. Rev. Lett. 115, 150402 (2015).
  21. M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, and A. Acín, Extractable Work from Correlations, Phys. Rev. X 5, 041011 (2015).
  22. M. H. Partovi, Entanglement versus Stosszahlansatz: Disappearance of the thermodynamic arrow in a high-correlation environment, Phys. Rev. E 77, 021110 (2008).
  23. D. Jennings and T. Rudolph, Entanglement and the thermodynamic arrow of time, Phys. Rev. E 81, 061130 (2010).
  24. M. Huber, M. Perarnau-Llobet, K. V. Hovhannisyan, P. Skrzypczyk, C. Klöckl, N. Brunner, and A. Acín, Thermodynamic cost of creating correlations, New J. Phys. 17, 065008 (2015).
  25. D. E. Bruschi, M. Perarnau-Llobet, N. Friis, K. V. Hovhannisyan, and M. Huber, The thermodynamics of creating correlations: Limitations and optimal protocols, Phys. Rev. E 91, 032118 (2015).
  26. S. Jevtic, D. Jennings, and T. Rudolph, Maximally and Minimally Correlated States Attainable within a Closed Evolving System, Phys. Rev. Lett. 108, 110403 (2012).
  27. M. Esposito and C. Van den Broeck, Second law and Landauer principle far from equilibrium, Europhys. Lett. 95, 40004 (2011).
  28. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80, 517 (2008).
  29. W. Pusz and S. L. Woronowicz, Passive states and KMS states for general quantum systems, Commun. Math. Phys. 58, 273 (1978).
  30. A. Lenard, Thermodynamical proof of the Gibbs formula for elementary quantum systems, J. Stat. Phys. 19, 575 (1978).
  31. P. Skrzypczyk, A. J. Short, and S. Popescu, Work extraction and thermodynamics for individual quantum systems, Nat. Commun. 5, 4185 (2014).
  32. J. Åberg, Truly work-like work extraction via a single-shot analysis, Nat. Commun. 4, 1925 (2013).
  33. D. Reeb and M. M. Wolf, An improved Landauer Principle with finite-size corrections, New J. Phys. 16, 103011 (2014).
  34. R. A. Bertlmann and P. Krammer, Bloch vectors for qudits, J. Phys. A: Math. Theor. 41, 235303 (2008).
  35. U. Fano, Pairs of two-level systems, Rev. Mod. Phys. 55, 855 (1983).
  36. P. Caban, K. Podlaski, J. Rembieliński, K. A. Smolińksi, and Z. Walczak, Entanglement and tensor product decomposition for two fermions, J. Phys. A: Math. Gen. 38, L79 (2005).
  37. M.-C. Bañuls, J. I. Cirac, and M. M. Wolf, Entanglement in fermionic systems, Phys. Rev. A 76, 022311 (2007).
  38. A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, Entanglement and Particle Identity: A Unifying Approach, Phys. Rev. Lett. 110, 080503 (2013).
  39. N. Friis, A. R. Lee, and D. E. Bruschi, Fermionic mode entanglement in quantum information, Phys. Rev. A 87, 022338 (2013).
  40. N. Friis, Reasonable fermionic quantum information theories require relativity, New J. Phys. 18, 033014 (2016).
  41. G. G. Amosov and S. N. Filippov, Spectral properties of reduced fermionic density operators and parity superselection rule, arXiv:1512.01828.
  42. C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621 (2012).
  43. G. Adesso, S. Ragy, and A. R. Lee, Continuous variable quantum information: Gaussian states and beyond, Open Syst. Inf. Dyn. 21, 1440001 (2014).
  44. N. Friis and I. Fuentes, Entanglement generation in relativistic quantum fields, J. Mod. Opt. 60, 22 (2013).
  45. D. E. Bruschi, A. R. Lee, and I. Fuentes, Time evolution techniques for detectors in relativistic quantum information, J. Phys. A: Math. Theor. 46, 165303 (2013).
  46. E. G. Brown, E. Martín-Martínez, N. C. Menicucci, and R. B. Mann, Detectors for probing relativistic quantum physics beyond perturbation theory, Phys. Rev. D 87, 084062 (2013).
  47. A. S. Holevo and R. F. Werner, Evaluating capacities of bosonic Gaussian channels, Phys. Rev. A 63, 032312 (2001).
  48. D. E. Bruschi, N. Friis, I. Fuentes, and S. Weinfurtner, On the robustness of entanglement in analogue gravity systems, New J. Phys. 15, 113016 (2013).

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