Entropy and Reversible Catalysis
Abstract
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 finitedimensional 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), 10.1103/PhysRevLett.122.210402]. They provide a complete singleshot 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 singleshot characterization of Gibbs states in quantum statistical mechanics.
 Publication:

Physical Review Letters
 Pub Date:
 December 2021
 DOI:
 10.1103/PhysRevLett.127.260402
 arXiv:
 arXiv:2012.05573
 Bibcode:
 2021PhRvL.127z0402W
 Keywords:

 Quantum Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Mathematics  Probability
 EPrint:
 5+5 pages