A Dynamical Approach to Non-Extensive Thermodynamics
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917327660908544 |
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| author | Lopes, Artur O. Varandas, Paulo |
| author_facet | Lopes, Artur O. Varandas, Paulo |
| contents | We develop a non-extensive thermodynamic formalism for the one-sided shift on a finite alphabet, inspired by Tsallis' generalization of Boltzmann entropy in statistical physics. We introduce notions of $q$-entropy, $q$-pressure, and $q$-transfer operators which extend the classical thermodynamic formalism when $q=1$. We prove a Bowen-type relation linking the $q$-pressure with a $(2-q)$-Ruelle transfer operator and show that $q$-equilibrium states correspond to classical equilibrium states for a related potential. We establish the existence and uniqueness of $q$-equilibrium states for Lipschitz potentials, prove the differentiability of the $q$-pressure, and obtain variational principles for both the $q$-pressure and a related asymptotic pressure. Finally, we study cohomological equations associated with $(2-q)$-transfer operators and prove the differentiable dependence of their solutions on the potential, yielding an alternative construction of eigenfunctions for classical Ruelle operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08896 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Dynamical Approach to Non-Extensive Thermodynamics Lopes, Artur O. Varandas, Paulo Dynamical Systems Statistical Mechanics Mathematical Physics Probability 37D35, 82B05, We develop a non-extensive thermodynamic formalism for the one-sided shift on a finite alphabet, inspired by Tsallis' generalization of Boltzmann entropy in statistical physics. We introduce notions of $q$-entropy, $q$-pressure, and $q$-transfer operators which extend the classical thermodynamic formalism when $q=1$. We prove a Bowen-type relation linking the $q$-pressure with a $(2-q)$-Ruelle transfer operator and show that $q$-equilibrium states correspond to classical equilibrium states for a related potential. We establish the existence and uniqueness of $q$-equilibrium states for Lipschitz potentials, prove the differentiability of the $q$-pressure, and obtain variational principles for both the $q$-pressure and a related asymptotic pressure. Finally, we study cohomological equations associated with $(2-q)$-transfer operators and prove the differentiable dependence of their solutions on the potential, yielding an alternative construction of eigenfunctions for classical Ruelle operators. |
| title | A Dynamical Approach to Non-Extensive Thermodynamics |
| topic | Dynamical Systems Statistical Mechanics Mathematical Physics Probability 37D35, 82B05, |
| url | https://arxiv.org/abs/2603.08896 |