Fundamental Limits of Control: A Quantum Approach to the Second Law

Kaiyuan Ji, Gilad Gour, Mark M. Wilde

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.

Anatoliy G. Butkovskiy, Yu. I. Samoilenko

Domenico D’Alessandro

Davide Girolami, Rebecca Schmidt, Gerardo Adesso

Cybernetics is a successful meta‐theory to model the regulation of complex systems from an abstract information‐theoretic viewpoint, regardless of the properties of the system under scrutiny. Fundamental limits to the controllability of an open system can be formalized in terms of the law of requisite variety, which is derived from the second law of thermodynamics and suggests that establishing correlations between the system of interest and a controller is beneficial. These concepts are briefly reviewed, and the chances, challenges and potential gains arising from the generalisation of such a framework to the quantum domain are discussed. image

Daniel P. Sheehan

The Second Law of Thermodynamics (the law of "increasing disorder") is fundamental to all the sciences and is considered inviolable by the general scientific community.[...]