A superstatistical measure of distance from canonical equilibrium
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910888969109504 |
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| author | Davis, Sergio |
| author_facet | Davis, Sergio |
| contents | Non-equilibrium systems in steady states are commonly described by generalized statistical mechanical theories such as non-extensive statistics and superstatistics. Superstatistics assumes that the inverse temperature $β= 1/(k_B T)$ follows some pre-established statistical distribution, however, it has been previously proved (Physica A 505, 864-870 [2018]) that $β$ cannot be associated to an observable function $B(\boldsymbolΓ)$ of the microstates $\boldsymbolΓ$. In this work, we provide an information-theoretical interpretation of this theorem by introducing a new quantity $\mathcal{D}$, the mutual information between $β$ and $\boldsymbolΓ$. Our results show that $\mathcal{D}$ is also a measure of departure from canonical equilibrium, and reveal a minimum, non-zero uncertainty about $β$ given $\boldsymbolΓ$ for every non-canonical superstatistical ensemble. This supports the use of the mutual information as a descriptor of complexity and correlation in complex systems, also providing in some cases a sound basis for the use of Tsallis' entropic index $q$ as a measure of distance from equilibrium, being in those cases a proxy for $\mathcal{D}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A superstatistical measure of distance from canonical equilibrium Davis, Sergio Statistical Mechanics Non-equilibrium systems in steady states are commonly described by generalized statistical mechanical theories such as non-extensive statistics and superstatistics. Superstatistics assumes that the inverse temperature $β= 1/(k_B T)$ follows some pre-established statistical distribution, however, it has been previously proved (Physica A 505, 864-870 [2018]) that $β$ cannot be associated to an observable function $B(\boldsymbolΓ)$ of the microstates $\boldsymbolΓ$. In this work, we provide an information-theoretical interpretation of this theorem by introducing a new quantity $\mathcal{D}$, the mutual information between $β$ and $\boldsymbolΓ$. Our results show that $\mathcal{D}$ is also a measure of departure from canonical equilibrium, and reveal a minimum, non-zero uncertainty about $β$ given $\boldsymbolΓ$ for every non-canonical superstatistical ensemble. This supports the use of the mutual information as a descriptor of complexity and correlation in complex systems, also providing in some cases a sound basis for the use of Tsallis' entropic index $q$ as a measure of distance from equilibrium, being in those cases a proxy for $\mathcal{D}$. |
| title | A superstatistical measure of distance from canonical equilibrium |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2402.09393 |