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AIP conference proceedings

Second Law of Thermodynamics with Discrete Quantum Feedback Control

Takahiro Sagawa, Masahito Ueda, Alexander I. Lvovsky

Published Jan 1, 2009• 6 citations
Publisher

Abstract

We propose a new thermodynamic inequality which leads to the maximum work that can be extracted from multi‐heat baths with the assistance of discrete quantum feedback control by “Maxwell’s demon.” The maximum work is determined by the free‐energy difference and a generalized mutual information content between the thermodynamic system and the feedback controller.

DOI
10.1063/1.3131311

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We propose a new thermodynamic inequality which leads to the maximum work that can be extracted from multi‐heat baths with the assistance of discrete quantum feedback control by “Maxwell’s demon.” The maximum work is determined by the free‐energy difference and a generalized mutual information content between the thermodynamic system and the feedback controller.
A new thermodynamic inequality is derived which leads to the maximum work that can be extracted from multi-heat-baths with the assistance of discrete quantum feedback control. The maximum work is determined by the free-energy difference and a generalized mutual information content between the thermodynamic system and the feedback controller. This maximum work can exceed that in conventional thermodynamics and, in the case of a heat cycle with two heat baths, the heat efficiency can be greater than that of the Carnot cycle. The consistency of our results with the second law of thermodynamics is ensured by the fact that work is needed for information processing of the feedback controller.
Recently Sagawa and Ueda [Phys. Rev. Lett. 100, 080403 (2008)] derived a bound on the work that can be extracted from a quantum system with the use of feedback control. They left open the question of whether this bound could be achieved for every measurement that could be made by the controller. We show that it can, and that this follows straightforwardly from recent work on Maxwell's demon by Alicki et al. [Open Syst. Inform. Dynam. 11, 205 (2004)], for both discrete and continuous feedback control. Our analysis also shows that bare, efficient measurements always do non-negative work on a system in equilibrium, but do not add heat.
Recently Sagawa and Ueda [Phys. Rev. Lett. 100, 080403 (2008)] derived a bound on the work that can be extracted from a quantum system with the use of feedback control. For many quantum measurements their bound was not tight. We show that a tight version of this bound follows straightforwardly from recent work on Maxwell's demon by Alicki et al. [Open Syst. Inf. Dyn. 11, 205 (2004)], for both discrete and continuous feedback control. Our analysis also shows that bare, efficient measurements always do non-negative work on a system in equilibrium, but do not add heat.
The study of feedback control inspired by Maxwell's demon has yielded fundamental insights into the relationship between thermodynamics and information. However, its fully quantum formulation, where the controller holds quantum side information that cannot be treated as a classical record, remains incomplete. In this paper, we establish fundamental no-go limits for thermodynamic state conversion while allowing quantum side information to be fed back to the system coherently. From two basic operational principles respected by all physically admissible feedback-control schemes, we derive the tightest possible bounds on the single-shot work of formation and extractable work for arbitrary quantum systems conditioned on arbitrary quantum side information. In the asymptotic limit, these bounds yield a generalized second law of thermodynamics with quantum feedback, governed by a conditional free energy. We further show that this generalized second law is consistent with the traditional second law once the acquisition, processing, and reset of side information are accounted for. These results extend information thermodynamics to the fully quantum regime and provide precise thermodynamic meanings for the negativity of single-shot conditional entropies.
We review a general theory of thermodynamics of information processing. The background of this topic is the recently-developed nonequilibrium statistical mechanics and quantum (and classical) information theory. These theories are closely related to the modern technologies to manipulate and observe small systems; for example, macromolecules and colloidal particles in the classical regime, and quantum-optical systems and quantum dots in the quantum regime. First, we review a generalization of the second law of thermodynamics to the situations in which small thermodynamic systems are subject to quantum feedback control. The generalized second law is expressed in terms of an inequality that includes the term of information obtained by the measurement, as well as the thermodynamic quantities such as the free energy. This inequality leads to the fundamental upper bound of the work that can be extracted by a “Maxwell's demon”, which can be regarded as a feedback controller with a memory that stores measurement outcomes. Second, we review generalizations of the second law of thermodynamics to the measurement and information erasure processes of the memory of the demon that is a quantum system. The generalized second laws consist of inequalities that identify the lower bounds of the energy costs that are needed for the measurement and the information erasure. The inequality for the erasure leads to the celebrated Landauer's principle for a special case. Moreover, these inequalities enable us to reconcile Maxwell's demon with the second law of thermodynamics. In these inequalities, thermodynamic quantities and information contents are treated on an equal footing. In fact, the inequalities are model-independent, so that they can be applied to a broad class of information processing. Therefore, these inequalities can be called the second law of “information thermodynamics”.