Details
| Original language | English |
|---|---|
| Article number | 241 |
| Journal | Entropy |
| Volume | 19 |
| Issue number | 6 |
| Publication status | Published - 23 May 2017 |
| Externally published | Yes |
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.
Keywords
- Correlations, Non-equilibrium free energy, Quantum relative entropy, Quantum thermodynamics
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Entropy, Vol. 19, No. 6, 241, 23.05.2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Axiomatic characterization of the quantum relative entropy and free energy
AU - Wilming, Henrik
AU - Gallego, Rodrigo
AU - Eisert, Jens
N1 - Funding Information: We acknowledge funding from the DFG (GA 2184/2-1), the BMBF, the EU (COST, AQuS), the ERC (TAQ) and the Studienstiftung des Deutschen Volkes.
PY - 2017/5/23
Y1 - 2017/5/23
N2 - 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.
AB - 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.
KW - Correlations
KW - Non-equilibrium free energy
KW - Quantum relative entropy
KW - Quantum thermodynamics
UR - http://www.scopus.com/inward/record.url?scp=85020522394&partnerID=8YFLogxK
U2 - 10.3390/e19060241
DO - 10.3390/e19060241
M3 - Article
AN - SCOPUS:85020522394
VL - 19
JO - Entropy
JF - Entropy
SN - 1099-4300
IS - 6
M1 - 241
ER -