Next Article in Journal
A Framework for Designing the Architectures of Deep Convolutional Neural Networks
Next Article in Special Issue
Deformed Jarzynski Equality
Previous Article in Journal
Maxwell’s Demon—A Historical Review
Previous Article in Special Issue
Kinetics of Interactions of Matter, Antimatter and Radiation Consistent with Antisymmetric (CPT-Invariant) Thermodynamics
Article Menu
Issue 6 (June) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(6), 241; doi:10.3390/e19060241

Axiomatic Characterization of the Quantum Relative Entropy and Free Energy

Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
*
Authors to whom correspondence should be addressed.
Academic Editor: Ronnie Kosloff
Received: 6 April 2017 / Revised: 3 May 2017 / Accepted: 16 May 2017 / Published: 23 May 2017
(This article belongs to the Special Issue Quantum Thermodynamics)
View Full-Text   |   Download PDF [249 KB, uploaded 23 May 2017]

Abstract

Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: (i) Continuity in the first argument; (ii) the validity of the data-processing inequality; (iii) additivity under tensor products; and (iv) super-additivity. This observation has immediate implications for quantum thermodynamics, which we discuss. Specifically, we demonstrate that, under reasonable restrictions, the free energy is singled out as a measure of athermality. In particular, we consider an extended class of Gibbs-preserving maps as free operations in a resource-theoretic framework, in which a catalyst is allowed to build up correlations with the system at hand. The free energy is the only extensive and continuous function that is monotonic under such free operations. View Full-Text
Keywords: quantum relative entropy; non-equilibrium free energy; quantum thermodynamics; correlations quantum relative entropy; non-equilibrium free energy; quantum thermodynamics; correlations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Wilming, H.; Gallego, R.; Eisert, J. Axiomatic Characterization of the Quantum Relative Entropy and Free Energy. Entropy 2017, 19, 241.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top