Explicit and covariant formula for thermodynamic volume in extended black hole thermodynamics
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911699206930432 |
|---|---|
| author | Xiao, Yong Liu, Yu-Xiao Tian, Yu Zhang, Hongbao |
| author_facet | Xiao, Yong Liu, Yu-Xiao Tian, Yu Zhang, Hongbao |
| contents | In extended black hole thermodynamics, the cosmological constant and other couplings are treated as thermodynamic variables, yielding the first law $\tildeδM = T\tildeδS+Ω\tildeδJ +\mathcal{V} \tildeδP+\cdots$, where $P\equiv -\fracΛ{8π}$. A long-standing conceptual gap in this framework is that, unlike $M$, $T$, $S$, $Ω$, and $J$, the thermodynamic volume $\mathcal{V} $ lacks a first-principles definition and can only be deduced from other thermodynamic quantities. This deficiency indicates that the underlying origin of $\mathcal{V} $ remains poorly understood. In this paper, we resolve this issue and provide an explicit, covariant formula for $\mathcal{V} $. We demonstrate that $\mathcal{V} $ (and the conjugate quantities of other couplings) universally decomposes into two contributions: one arising from the explicit coupling dependence of the Lagrangian, and the other from the response of the fundamental dynamical fields. This clarifies the physical meaning of the thermodynamic volume and places it on the same footing as other intrinsic thermodynamic quantities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01916 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit and covariant formula for thermodynamic volume in extended black hole thermodynamics Xiao, Yong Liu, Yu-Xiao Tian, Yu Zhang, Hongbao General Relativity and Quantum Cosmology High Energy Physics - Theory In extended black hole thermodynamics, the cosmological constant and other couplings are treated as thermodynamic variables, yielding the first law $\tildeδM = T\tildeδS+Ω\tildeδJ +\mathcal{V} \tildeδP+\cdots$, where $P\equiv -\fracΛ{8π}$. A long-standing conceptual gap in this framework is that, unlike $M$, $T$, $S$, $Ω$, and $J$, the thermodynamic volume $\mathcal{V} $ lacks a first-principles definition and can only be deduced from other thermodynamic quantities. This deficiency indicates that the underlying origin of $\mathcal{V} $ remains poorly understood. In this paper, we resolve this issue and provide an explicit, covariant formula for $\mathcal{V} $. We demonstrate that $\mathcal{V} $ (and the conjugate quantities of other couplings) universally decomposes into two contributions: one arising from the explicit coupling dependence of the Lagrangian, and the other from the response of the fundamental dynamical fields. This clarifies the physical meaning of the thermodynamic volume and places it on the same footing as other intrinsic thermodynamic quantities. |
| title | Explicit and covariant formula for thermodynamic volume in extended black hole thermodynamics |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.01916 |