Entropy alternatives for equilibrium and out of equilibrium systems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912306184585216 |
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| author | Vogel, Eugenio E. Peña, Francisco J. Saravia, G. Vargas, P. |
| author_facet | Vogel, Eugenio E. Peña, Francisco J. Saravia, G. Vargas, P. |
| contents | We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a dynamical entropy measure. To present the scope and advantages of these quantities, we analyze two distinct systems: (a) Monte Carlo simulations of magnetic moments on a square lattice and (b) seismic time series from the United States Geological Survey catalog. Both systems are well-established in the literature, serving as robust benchmarks. Shannon entropy is employed as a reference point to assess the similarities and differences with the proposed measures. A key distinction lies in the sensitivity of non-repeatability and mutability to the temporal ordering of data, which contrasts with traditional entropy definitions. Moreover, \textit{sorted mutability} -- the mutability computed from a reordered data version -- reveals additional insights into the critical behavior of the systems under study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24186 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entropy alternatives for equilibrium and out of equilibrium systems Vogel, Eugenio E. Peña, Francisco J. Saravia, G. Vargas, P. Statistical Mechanics Disordered Systems and Neural Networks We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a dynamical entropy measure. To present the scope and advantages of these quantities, we analyze two distinct systems: (a) Monte Carlo simulations of magnetic moments on a square lattice and (b) seismic time series from the United States Geological Survey catalog. Both systems are well-established in the literature, serving as robust benchmarks. Shannon entropy is employed as a reference point to assess the similarities and differences with the proposed measures. A key distinction lies in the sensitivity of non-repeatability and mutability to the temporal ordering of data, which contrasts with traditional entropy definitions. Moreover, \textit{sorted mutability} -- the mutability computed from a reordered data version -- reveals additional insights into the critical behavior of the systems under study. |
| title | Entropy alternatives for equilibrium and out of equilibrium systems |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2410.24186 |