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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.23257 |
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| _version_ | 1866917365498773504 |
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| author | Trindade, Marco A. S. |
| author_facet | Trindade, Marco A. S. |
| contents | In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual q-information, and establish several inequalities analogous to those of classical information theory. Within the context of Markov chains, these results are employed to prove a version of the second law of thermodynamics. Furthermore, we investigate the maximum entropy method in this setting. Finally, we prove a Tsallis version of the Shannon-McMillan-Breiman theorem and discuss the implications of these results in nonextensive statistical physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23257 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Information-theoretic structure for the Tsallis q-entropy in statistical physics Trindade, Marco A. S. Mathematical Physics In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual q-information, and establish several inequalities analogous to those of classical information theory. Within the context of Markov chains, these results are employed to prove a version of the second law of thermodynamics. Furthermore, we investigate the maximum entropy method in this setting. Finally, we prove a Tsallis version of the Shannon-McMillan-Breiman theorem and discuss the implications of these results in nonextensive statistical physics. |
| title | Information-theoretic structure for the Tsallis q-entropy in statistical physics |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2603.23257 |