https://doi.org/10.1140/epjp/s13360-024-04972-z
Regular Article
Unified catalytic entropy principles of general states
1
School of Information Science and Technology, Southwest Jiaotong University, 610031, Chengdu, China
2
School of Electronic Engineering, Dublin City University, Dublin 9, Ireland
Received:
1
July
2022
Accepted:
2
February
2024
Published online:
14
February
2024
The second law of thermodynamics dictates that entropy tends to increase, leading to a notion of disorder in thermostatistics. This principle applies to both quantum thermostatistics, where the von Neumann entropy is used, and nonextensive quantum thermostatistics, which employs the Tsallis entropy. In this work, we provide operational characterizations of general entropy measures by utilizing catalytic transformations or dephasing operations on unknown states. We introduce a catalytic principle that aligns with the second law of thermodynamics, encompassing both quantum thermostatistics and nonextensive quantum thermostatistics. This principle uncovers novel features that go beyond the second law of thermodynamics by maximizing the cross-entropy during irreversible catalytic procedures. Our findings have practical implications for asymptotic tasks such as universal quantum source encoding, even when only incomplete information is available. We apply these results to single-shot state transitions.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjp/s13360-024-04972-z.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.