How to Reconcile Maxwell’s Demon with the Second Law?_

How to Reconcile Maxwell’s Demon with the Second Law?

Ever since the nineteenth century, Maxwell’s demon has attracted a lot of attentions concerning the foundation of the second law of thermodynamics [1]. Recently, the demon has been experimentally realized [2]. The demon can adiabatically decrease the entropy of thermodynamic systems by feedback control, which seems to be a violation of the second law. A crucial question is: What reconciles the demon with the second law? In this talk, I will answer this question on the basis of our recent theoretical works [3-5]. First, I will introduce the basic concepts in information theory and nonequilibrium thermodynamics. Second, I will show that, on the basis of generalized Jarzynski equalities, the positive entropy production during measurement compensates for the negative entropy production during feedback control. Third, I will briefly review the history of Maxwell’s demon, and clarify the consistency between our results and previous researches. Our results constitute the second law of « information thermodynamics, » in which thermodynamic quantities and information contents are treated on an equal footing.

[1] « Maxwell’s demon 2: Entropy, Classical and Quantum Information, Computing, » H. S. Leff and A. F. Rex (eds.), (Princeton University Press, New Jersey, 2003).

[2] S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Nature Physics 6, 988-992 (2010).

[3] T. Sagawa and M. Ueda, Phys. Rev. Lett. 102, 250602 (2009).

[4] T. Sagawa and M. Ueda, Phys. Rev. Lett. 104, 198904 (2010).

[5] T. Sagawa and M. Ueda, arXiv:1206.2479 (2012).

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