A new axiomatic characterization of the von Neumann entropy

P. Staszewski

Xiaofei Qi, Ting Zhang

Noah Linden, Andreas Winter

Dėnes Petz

Mirjam Weilenmann, Lea Krämer, Philippe Faist +1 more

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E. H. Lieb and J. Yngvason Proc. R. Soc. 469, 20130408 (2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalization to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in nonequilibrium thermodynamics correspond to entropies used in one-shot information theory.

Oliver Rudolph

We obtain a mathematically simple characterization of all functionals coinciding with the von Neumann reduced entropy on pure states based on the Khinchin–Faddeev axiomatization of Shannon entropy and give a physical interpretation of the axioms in terms of entanglement.