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arXiv · 2103.08681

What is Entropy? A new perspective from games of chance

Sarah Brandsen·Isabelle Jianing Geng·Gilad Gour
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Abstract

Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of a physical system, as a system's performance in gambling games depends solely on the uncertainty of its output. In this work, we construct families of games which induce pre-orders corresponding to majorization, conditional majorization, and channel majorization. Finally, we provide operational interpretations for all pre-orders, show the relevance of these results to dynamical resource theories, and find the only asymptotically continuous classical dynamic entropy.

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Sarah Brandsen, Isabelle Jianing Geng, Gilad Gour. 2021-03-15. What is Entropy? A new perspective from games of chance. https://doi.org/10.1103/physreve.105.024117

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