Chaos, the Critical Phenomenon in Phase Space: Feigenbaum Constants and Critical Exponents
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918331803500544 |
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| author | Xia, Yonghui Feng, Hongtao |
| author_facet | Xia, Yonghui Feng, Hongtao |
| contents | Chaos in both dissipative systems and conservative systems is investigated on the approach of renormalization group. It is found that the chaos is regarded as the critical phenomenon of equilibrium statistics in phase space. The two Feigenbaum constants in the period-doubling bifurcation systems correspond to two independent critical exponents, which are universal and can be adopted to distinguish the classes of chaos. For the conservative systems, due to the critical nature of the chaos, the isolated systems with different parameters are correlated in the phase space, and therefore the isolated system is no longer isolated in the phase space. The information of conservative systems is irreversibly lost over time, which leads to the increase entropy in an isolated system, and the contradiction between the second law of thermodynamics and the reversibility of isolated systems can be resolved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08895 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chaos, the Critical Phenomenon in Phase Space: Feigenbaum Constants and Critical Exponents Xia, Yonghui Feng, Hongtao Chaotic Dynamics Statistical Mechanics Chaos in both dissipative systems and conservative systems is investigated on the approach of renormalization group. It is found that the chaos is regarded as the critical phenomenon of equilibrium statistics in phase space. The two Feigenbaum constants in the period-doubling bifurcation systems correspond to two independent critical exponents, which are universal and can be adopted to distinguish the classes of chaos. For the conservative systems, due to the critical nature of the chaos, the isolated systems with different parameters are correlated in the phase space, and therefore the isolated system is no longer isolated in the phase space. The information of conservative systems is irreversibly lost over time, which leads to the increase entropy in an isolated system, and the contradiction between the second law of thermodynamics and the reversibility of isolated systems can be resolved. |
| title | Chaos, the Critical Phenomenon in Phase Space: Feigenbaum Constants and Critical Exponents |
| topic | Chaotic Dynamics Statistical Mechanics |
| url | https://arxiv.org/abs/2602.08895 |