TY - JOUR

T1 - Entropy and Reversible Catalysis

AU - Wilming, H.

N1 - Funding Information: I would like to thank Paul Boes, Rodrigo Gallego, Markus P. Müller, and Ivan Sergeev for extensive discussions about the catalytic entropy conjecture. In particular, I would like to thank Paul Boes for useful comments on an earlier draft and for suggesting how the proof of the quantum result can be transferred to the classical setting. I would further like to thank Joe Renes for pointing me to Ref. . This research was supported by the Swiss National Science Foundation through the National Centre of Competence in Research Quantum Science and Technology (QSIT).

PY - 2021/12/24

Y1 - 2021/12/24

N2 - I show that nondecreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst,"whose state has to remain invariant exactly in the transition. This statement is proven both in the case of finite-dimensional quantum mechanics, where von Neumann entropy is the relevant entropy, and in the case of systems whose states are described by probability distributions on finite sample spaces, where Shannon entropy is the relevant entropy. The results give an affirmative resolution to the (approximate) catalytic entropy conjecture introduced by Boes et al. [Phys. Rev. Lett. 122, 210402 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.210402]. They provide a complete single-shot characterization without external randomness of von Neumann entropy and Shannon entropy. I also compare the results to the setting of phenomenological thermodynamics and show how they can be used to obtain a quantitative single-shot characterization of Gibbs states in quantum statistical mechanics.

AB - I show that nondecreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst,"whose state has to remain invariant exactly in the transition. This statement is proven both in the case of finite-dimensional quantum mechanics, where von Neumann entropy is the relevant entropy, and in the case of systems whose states are described by probability distributions on finite sample spaces, where Shannon entropy is the relevant entropy. The results give an affirmative resolution to the (approximate) catalytic entropy conjecture introduced by Boes et al. [Phys. Rev. Lett. 122, 210402 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.210402]. They provide a complete single-shot characterization without external randomness of von Neumann entropy and Shannon entropy. I also compare the results to the setting of phenomenological thermodynamics and show how they can be used to obtain a quantitative single-shot characterization of Gibbs states in quantum statistical mechanics.

UR - http://www.scopus.com/inward/record.url?scp=85122503671&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.127.260402

DO - 10.1103/PhysRevLett.127.260402

M3 - Article

C2 - 35029463

AN - SCOPUS:85122503671

VL - 127

JO - Physical review letters

JF - Physical review letters

SN - 0031-9007

IS - 26

M1 - 260402

ER -