Abstract
In this chapter, we derive a generalized second law with a quantum measurement and quantum feedback control [1, 2], which is the first main part of this thesis. Thermodynamics of feedback control has been studied for a long time in terms of Maxwell’s demon [3–7]. In fact, the demon can be formulated as a feedback controller acting on thermodynamic systems. Recently, this topic has attracted numerous attentions based on the advancements in nonequilibrium statistical mechanics and quantum information theory [1, 2, 8–21]. In Sect. 6.1, we derive the lower bound of the entropy difference by feedback control. Based on it, in Sect. 6.2, we derive a generalized second law of thermodynamics with feedback control. In Sect. 6.3, we discuss a generalized Szilard engine [22] that achieves the upper bound of the generalized second law.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
T. Sagawa, M. Ueda, Phys. Rev. Lett. 100, 080403 (2008)
T. Sagawa, Prog. Theor. Phys. 127, 1 (2012)
J.C. Maxwell, Theory of Heat (Appleton, London, 1871)
H.S. Leff, A.F. Rex (eds.), Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing (Princeton University Press, Princeton, 2003)
K. Maruyama, F. Nori, V. Vedral, Rev. Mod. Phys. 81, 1 (2009)
O.J.E. Maroney, Information processing and thermodynamic entropy, in The Stanford Encyclopedia of Philosophy, Fall 2009 edn., ed. by E.N. Zalta (Fall, Chicago, 2009).
T. Sagawa, M Ueda, Information thermodynamics: maxwell’s demon in nonequilibrium dynamics, in: Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond. R. Klages, W. Just, C. and Jarzynski (Eds.),(Wiley, Weinheim, 2012) e-print : arXiv:1111.5769 (2011)(to appear).
S. Lloyd, Phys. Rev. A 39, 5378 (1989)
S. Lloyd, Phys. Rev. A 56, 3374 (1997)
M.A. Nielsen, C.M. Caves, B. Schumacher, H. Barnum, Proc. R. Soc. London A 454, 277 (1998)
W.H. Zurek, arXiv:quant-ph/0301076 (2003).
T.D. Kieu, Phys. Rev. Lett. 93, 140403 (2004)
A.E. Allahverdyan, R. Balian, ThM Nieuwenhuizen, J. Mod. Opt. 51, 2703 (2004)
H.T. Quan, Y.D. Wang, Y-x. Liu, C. P. Sun, F. Nori. Phys. Rev. Lett. 97, 180402 (2006)
K. Jacobs, Phys. Rev. A 80, 012322 (2009)
S.W. Kim, T. Sagawa, S. De Liberato, M. Ueda, Phys. Rev. Lett. 106, 070401 (2011)
Y. Morikuni, H. Tasaki, J. Stat. Phys. 143, 1 (2011)
H. Dong, D.Z. Xu, C.Y. Cai, C.P. Sun, Phys. Rev. E 83, 061108 (2011)
D.V. Averin, M. Möttönen, J.P. Pekola, Phys. Rev. B 84, 245448 (2011)
S. Lahiri, S. Rana, A.M. Jayannavar, J. Phys. A: Math. Theor. 45, 065002 (2012)
Y. Lu, G.L. Long, Phys. Rev. E 85, 011125 (2012)
T. Sagawa, M. Ueda, Phys. Rev. E 85, 021104 (2012)
H.M. Wiseman, G.J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2010)
L. Szilard, Z. Phys. 53, 840 (1929)
D. Abreu, U. Seifert, Europhys. Lett. 94, 10001 (2011)
J.M. Horowitz, J.M.R. Parrondo, New J. Phys. 13, 123019 (2011)
H.J. Groenewold, Int. J. Theor. Phys. 4, 327 (1971)
M. Ozawa, J. Math. Phys. 27, 759 (1986)
F. Buscemi, M. Hayashi, M. Horodecki, Phys. Rev. Lett. 100, 210504 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Japan
About this chapter
Cite this chapter
Sagawa, T. (2012). Second Law with Feedback Control. In: Thermodynamics of Information Processing in Small Systems. Springer Theses. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54168-4_6
Download citation
DOI: https://doi.org/10.1007/978-4-431-54168-4_6
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-54167-7
Online ISBN: 978-4-431-54168-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)