Fundamental temperature in the superstatistical description of non-equilibrium steady states
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914486569402368 |
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| author | Davis, Sergio |
| author_facet | Davis, Sergio |
| contents | Among the statistical mechanical frameworks able to describe systems in non-equilibrium steady states such as collisionless plasmas, self-gravitating systems and other complex systems, superstatistics have gained recent attention. Superstatistics postulates a superposition of canonical systems with inverse temperatures $β$ described by a probability distribution depending on the external conditions. Unfortunately, the uncertainty about $β$ cannot be attributed to fluctuations of a phase space function, and this suggests that the distribution of $β$ is purely of statistical nature and must be inferred rather than measured. This lack of direct observability of the superstatistical temperature then becomes a conceptual issue in need of resolution. In this work we address this issue, showing that a mapping exists between functions of the superstatistical temperature and functions of the recently proposed fundamental temperature, a model-dependent function of the energy, in such a way that their expectation values coincide. We illustrate the use of this mapping by computing the conditional distribution of inverse temperature given energy for the $q$-canonical ensemble, as well as the full inverse temperature distribution, without the use of Laplace inversion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17035 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fundamental temperature in the superstatistical description of non-equilibrium steady states Davis, Sergio Statistical Mechanics Among the statistical mechanical frameworks able to describe systems in non-equilibrium steady states such as collisionless plasmas, self-gravitating systems and other complex systems, superstatistics have gained recent attention. Superstatistics postulates a superposition of canonical systems with inverse temperatures $β$ described by a probability distribution depending on the external conditions. Unfortunately, the uncertainty about $β$ cannot be attributed to fluctuations of a phase space function, and this suggests that the distribution of $β$ is purely of statistical nature and must be inferred rather than measured. This lack of direct observability of the superstatistical temperature then becomes a conceptual issue in need of resolution. In this work we address this issue, showing that a mapping exists between functions of the superstatistical temperature and functions of the recently proposed fundamental temperature, a model-dependent function of the energy, in such a way that their expectation values coincide. We illustrate the use of this mapping by computing the conditional distribution of inverse temperature given energy for the $q$-canonical ensemble, as well as the full inverse temperature distribution, without the use of Laplace inversion. |
| title | Fundamental temperature in the superstatistical description of non-equilibrium steady states |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2604.17035 |