Duality between dissipation-coherence trade-off and thermodynamic speed limit based on thermodynamic uncertainty relation for stochastic limit cycles
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909005513752576 |
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| author | Nagayama, Ryuna Ito, Sosuke |
| author_facet | Nagayama, Ryuna Ito, Sosuke |
| contents | We derive two fundamental trade-offs for general stochastic limit cycles in the weak-noise limit. The first is the dissipation-coherence trade-off, which was discovered and proved under additional assumptions by Santolin and Falasco [Phys. Rev. Lett. 135, 057101 (2025)]. This trade-off bounds the entropy production required for one oscillatory period using the number of oscillations that occur before steady-state correlations are disrupted. The second is the thermodynamic speed limit, which bounds the entropy production by the Euclidean length of the limit cycle. These trade-offs are obtained by substituting mutually dual observables, derived from the stability of the limit cycle, into the thermodynamic uncertainty relation. This fact allows us to regard the dissipation-coherence trade-off as the dual of the thermodynamic speed limit. We numerically demonstrate these trade-offs using the noisy Rössler model. We also apply the trade-offs to stochastic chemical systems, where the diffusion coefficient matrix may contain zero eigenvalues. Furthermore, we show that the dissipation-coherence trade-off is always achievable by appropriately modifying the diffusion coefficient matrix based on the phase reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Duality between dissipation-coherence trade-off and thermodynamic speed limit based on thermodynamic uncertainty relation for stochastic limit cycles Nagayama, Ryuna Ito, Sosuke Statistical Mechanics We derive two fundamental trade-offs for general stochastic limit cycles in the weak-noise limit. The first is the dissipation-coherence trade-off, which was discovered and proved under additional assumptions by Santolin and Falasco [Phys. Rev. Lett. 135, 057101 (2025)]. This trade-off bounds the entropy production required for one oscillatory period using the number of oscillations that occur before steady-state correlations are disrupted. The second is the thermodynamic speed limit, which bounds the entropy production by the Euclidean length of the limit cycle. These trade-offs are obtained by substituting mutually dual observables, derived from the stability of the limit cycle, into the thermodynamic uncertainty relation. This fact allows us to regard the dissipation-coherence trade-off as the dual of the thermodynamic speed limit. We numerically demonstrate these trade-offs using the noisy Rössler model. We also apply the trade-offs to stochastic chemical systems, where the diffusion coefficient matrix may contain zero eigenvalues. Furthermore, we show that the dissipation-coherence trade-off is always achievable by appropriately modifying the diffusion coefficient matrix based on the phase reduction. |
| title | Duality between dissipation-coherence trade-off and thermodynamic speed limit based on thermodynamic uncertainty relation for stochastic limit cycles |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2509.06421 |