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arXiv:2206.15340

Work Extracting From Nonextensive Small System With Feedback and Second Law-Like Inequalities with Quantum Tsallis Entropy

Amiri, Saman, Mirzaee, Mahdi, Mohammad Mazhari

Published Jun 30, 2022• 0 citations
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Abstract

Gibbs-Boltzmann entropy leads to systems that have a strong dependence on initial conditions. In reality, most materials behave quite independently of initial conditions. Nonextensive entropy or Tsallis entropy leads to nonextensive statistical mechanics. In this paper, we calculate the Tsallis form of Clausius inequality and then determine the upper bound for extracting work from the small system in the nonextensive statistical mechanics with mutual information. In the following, we extract mutual information and adjust Maxwell's demon with quantum feedback control.

DOI
10.48550/arxiv.2206.15340

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Gibbs-Boltzmann entropy leads to systems that have a strong dependence on initial conditions. In reality, most materials behave quite independently of initial conditions. Nonextensive entropy or Tsallis entropy leads to nonextensive statistical mechanics. In this paper, we calculate the Tsallis form of Clausius inequality and then determine the upper bound for extracting work from the small system in the nonextensive statistical mechanics with mutual information. In the following, we extract mutual information and adjust Maxwell's demon with quantum feedback control.
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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.