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Unified catalytic entropy principles of general states

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Abstract

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.

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Notes

  1. Supplementary Information including the proof of Theorem 1 for different quantum entropies including Refs. [1, 11, 12, 14, 21,22,23,24,25, 28,29,30,31,32,33,34,35,36,37,38,39,40].

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 62172341), Sichuan Natural Science Foundation (No. 2023JQ00447), and Interdisciplinary Research of Southwest Jiaotong University China (No. 2682022KJ004).

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Authors and Affiliations

  1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 610031, China

    Ming-Xing Luo

  2. School of Electronic Engineering, Dublin City University, Dublin 9, Ireland

    Xiaojun Wang

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  1. Ming-Xing Luo
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Correspondence to Ming-Xing Luo.

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Luo, MX., Wang, X. Unified catalytic entropy principles of general states. Eur. Phys. J. Plus 139, 160 (2024). https://doi.org/10.1140/epjp/s13360-024-04972-z

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