On the local thermodynamic relations in relativistic spin hydrodynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914598410518528 |
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| author | Becattini, Francesco Singh, Rajeev |
| author_facet | Becattini, Francesco Singh, Rajeev |
| contents | We demonstrate, by providing two specific examples, that the local differential thermodynamic relations used as educated guesses in relativistic hydrodynamics with spin, do not hold even at global thermodynamic equilibrium. We show, by using a rigorous quantum statistical method, that for massless free fermions and massive free fermions with rotation and acceleration at global thermodynamic equilibrium, the derivative of the pressure function with respect to the spin potential differs from the spin density and acquires a correction of the same order. Such correction cannot be eliminated by any redefinition of the entropy current, a so-called entropy-gauge transformation. Therefore, for an accurate determination of the constitutive relations in relativistic spin hydrodynamics, the traditional method of assuming differential thermodynamic relations is not appropriate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_20681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the local thermodynamic relations in relativistic spin hydrodynamics Becattini, Francesco Singh, Rajeev Nuclear Theory High Energy Physics - Theory We demonstrate, by providing two specific examples, that the local differential thermodynamic relations used as educated guesses in relativistic hydrodynamics with spin, do not hold even at global thermodynamic equilibrium. We show, by using a rigorous quantum statistical method, that for massless free fermions and massive free fermions with rotation and acceleration at global thermodynamic equilibrium, the derivative of the pressure function with respect to the spin potential differs from the spin density and acquires a correction of the same order. Such correction cannot be eliminated by any redefinition of the entropy current, a so-called entropy-gauge transformation. Therefore, for an accurate determination of the constitutive relations in relativistic spin hydrodynamics, the traditional method of assuming differential thermodynamic relations is not appropriate. |
| title | On the local thermodynamic relations in relativistic spin hydrodynamics |
| topic | Nuclear Theory High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.20681 |