By-passing fluctuation theorems

Paul Boes1, Rodrigo Gallego1, Nelly H. Y. Ng1, Jens Eisert1, and Henrik Wilming2

1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
2Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

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Abstract

Fluctuation theorems impose constraints on possible work extraction probabilities in thermodynamical processes. These constraints are stronger than the usual second law, which is concerned only with average values. Here, we show that such constraints, expressed in the form of the Jarzysnki equality, can be by-passed if one allows for the use of catalysts---additional degrees of freedom that may become correlated with the system from which work is extracted, but whose reduced state remains unchanged so that they can be re-used. This violation can be achieved both for small systems but also for macroscopic many-body systems, and leads to positive work extraction per particle with finite probability from macroscopic states in equilibrium. In addition to studying such violations for a single system, we also discuss the scenario in which many parties use the same catalyst to induce local transitions. We show that there exist catalytic processes that lead to highly correlated work distributions, expected to have implications for stochastic and quantum thermodynamics.

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► References

[1] C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).
https:/​/​doi.org/​10.1103/​PhysRevLett.78.2690

[2] G. E. Crooks, J. Stat. Phys. 90, 1481 (1998).
https:/​/​doi.org/​10.1023/​A:1023208217925

[3] H. Tasaki, ArXiv e-prints (2000), arXiv:1303.6393.
arXiv:1303.6393

[4] P. Erker, M. T. Mitchison, R. Silva, M. P. Woods, N. Brunner, and M. Huber, Phys. Rev. X 7, 031022 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.031022

[5] M. P. Woods, R. Silva, and J. Oppenheim, Ann Hen. Poin. 20, 125 (2019).
https:/​/​doi.org/​10.1007/​s00023-018-0736-9

[6] F. G. S. L. Brandão, M. Horodecki, N. H. Y. Ng, J. Oppenheim, and S. Wehner, PNAS 112, 3275 (2015).
https:/​/​doi.org/​10.1073/​pnas.1411728112

[7] N. H. Y. Ng, L. Mančinska, C. Cirstoiu, J. Eisert, and S. Wehner, New J. Phys. 17, 085004 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​8/​085004

[8] M. P. Müller, Phys. Rev. X 8 (2018), 10.1103/​physrevx.8.041051.
https:/​/​doi.org/​10.1103/​physrevx.8.041051

[9] P. Boes, J. Eisert, R. Gallego, M. P. Mueller, and H. Wilming, Phys. Rev. Lett. 122, 210402 (2019).
https:/​/​doi.org/​10.1103/​physrevlett.122.210402

[10] C. Jarzynski, Annu. Rev. Condens. Matter Phys. 2, 329 (2011).
https:/​/​doi.org/​10.1007/​978-3-0348-0359-5_4

[11] V. Cavina, A. Mari, and V. Giovannetti, Scientific Rep. 6, 29282 (2016).
https:/​/​doi.org/​10.1038/​srep29282

[12] O. Maillet et al., Phys. Rev. Lett. 122, 150604 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.150604

[13] A. E. Rastegin, J. Stat. Mech. 2013, P06016 (2013).
https:/​/​doi.org/​10.1088/​1742-5468/​2013/​06/​P06016

[14] A. E. Rastegin and K. Życzkowski, Phys. Rev. E 89, 012127 (2014).
https:/​/​doi.org/​10.1103/​PhysRevE.89.012127

[15] H. Wilming, R. Gallego, and J. Eisert, Entropy 19, 241 (2017).
https:/​/​doi.org/​10.3390/​e19060241

[16] P. Boes, H. Wilming, R. Gallego, and J. Eisert, Phys. Rev. X 8, 041016 (2018).
https:/​/​doi.org/​10.1103/​PhysRevX.8.041016

[17] Á. M. Alhambra, M. Lostaglio, and C. Perry, Quantum 3, 188 (2019).
https:/​/​doi.org/​10.22331/​q-2019-09-23-188

[18] C. Sparaciari, D. Jennings, and J. Oppenheim, Nat. Commun. 8, 1895 (2017).
https:/​/​doi.org/​10.1038/​s41467-017-01505-4

[19] K. M. R. Audenaert and S. Scheel, New J. Phys. 10, 023011 (2008).
https:/​/​doi.org/​10.1088/​1367-2630/​10/​2/​023011

[20] A. Lenard, J. Stat. Phys. 19, 575 (1978).
https:/​/​doi.org/​10.1007/​BF01011769

[21] W. Pusz and S. L. Woronowicz, Comm. Math. Phys. 58, 273 (1978).
https:/​/​doi.org/​10.1007/​BF01614224

[22] K. Huang, Statistical mechanics (Wiley, 1987).
https:/​/​doi.org/​10.1063/​1.3047170

[23] P. Talkner, P. Hänggi, and M. Morillo, Phys. Rev. E 77, 051131 (2008).
https:/​/​doi.org/​10.1103/​PhysRevE.77.051131

[24] M. Lostaglio, M. P. Müller, and M. Pastena, Phys. Rev. Lett. 115, 150402 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.150402

[25] T. Sagawa and M. Ueda, Phys. Rev. Lett. 109, 180602 (2012a).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.180602

[26] T. Sagawa and M. Ueda, New J. Phys. 15, 125012 (2013).
https:/​/​doi.org/​10.1088/​1367-2630/​15/​12/​125012

[27] T. Sagawa and M. Ueda, Phys. Rev. Lett. 109, 180602 (2012b).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.180602

[28] S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Nature Phys. 6, 988 (2010).
https:/​/​doi.org/​10.1038/​nphys1821

[29] M. Horodecki and J. Oppenheim, Nature Comm. 4, 2059 (2013).
https:/​/​doi.org/​10.1038/​ncomms3059

[30] C. Perry, P. Ć wikliński, J. Anders, M. Horodecki, and J. Oppenheim, Phys. Rev. X 8, 041049 (2018).
https:/​/​doi.org/​10.1103/​PhysRevX.8.041049

[31] P. Faist, J. Oppenheim, and R. Renner, New J. Phys. 17, 043003 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​4/​043003

[32] C. Gogolin, M. P. Müller, and J. Eisert, Phys. Rev. Lett. 106, 040401 (2011).
https:/​/​doi.org/​10.1103/​PhysRevLett.106.040401

[33] A. Anshu, New J. Phys. 18, 083011 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​8/​083011

[34] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
https:/​/​doi.org/​10.1119/​1.1463744

[35] S. Goldstein, T. Hara, and H. Tasaki, ArXiv e-prints (2013), arXiv:1303.6393.
arXiv:1303.6393

[36] M. Kliesch, C. Gogolin, M. J. Kastoryano, A. Riera, and J. Eisert, Phys. Rev. X 4, 031019 (2014).
https:/​/​doi.org/​10.1103/​PhysRevX.4.031019

[37] J. Watrous, The theory of quantum information (Cambridge University Press, 2018).
https:/​/​doi.org/​10.1017/​9781316848142

[38] M. Perarnau-Llobet, E. Bäumer, K. V. Hovhannisyan, M. Huber, and A. Acin, Phys. Rev. Lett. 118, 070601 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.070601

[39] J. V. Koski, V. F. Maisi, T. Sagawa, and J. P. Pekola, Phys. Rev. Lett. 113, 030601 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.113.030601

Cited by

[1] Matteo Lostaglio, "An introductory review of the resource theory approach to thermodynamics", Reports on Progress in Physics 82 11, 114001 (2019).

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