Dissipation anomaly in gradient-driven nonequilibrium steady states
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909917161455616 |
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| author | Nakano, Hiroyoshi Minami, Yuki |
| author_facet | Nakano, Hiroyoshi Minami, Yuki |
| contents | Dissipation anomaly-the persistence of finite energy dissipation in the inviscid limit-is a hallmark of turbulence, sometimes regarded as the "zeroth law" of turbulent flows. Here, we demonstrate that this phenomenon is not exclusive to turbulence. Using fluctuating hydrodynamics, we show that a simple gradient-driven nonequilibrium steady state, in which a fluid is subjected to a constant scalar gradient but remains macroscopically quiescent, also exhibits dissipation anomaly. Direct numerical simulations and self-consistent mode-coupling theory reveal that the anomaly originates from giant, long-range nonequilibrium fluctuations amplified by the imposed gradient. While linear theory predicts a divergent dissipation in the inviscid limit, nonlinear mode coupling regularizes the divergence, yielding a finite anomalous dissipation. Our findings identify a new, non-turbulent arena for dissipation anomaly and establish the interplay between thermal noise and nonequilibrium driving as a fundamental route to singular behavior in hydrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dissipation anomaly in gradient-driven nonequilibrium steady states Nakano, Hiroyoshi Minami, Yuki Statistical Mechanics Fluid Dynamics Dissipation anomaly-the persistence of finite energy dissipation in the inviscid limit-is a hallmark of turbulence, sometimes regarded as the "zeroth law" of turbulent flows. Here, we demonstrate that this phenomenon is not exclusive to turbulence. Using fluctuating hydrodynamics, we show that a simple gradient-driven nonequilibrium steady state, in which a fluid is subjected to a constant scalar gradient but remains macroscopically quiescent, also exhibits dissipation anomaly. Direct numerical simulations and self-consistent mode-coupling theory reveal that the anomaly originates from giant, long-range nonequilibrium fluctuations amplified by the imposed gradient. While linear theory predicts a divergent dissipation in the inviscid limit, nonlinear mode coupling regularizes the divergence, yielding a finite anomalous dissipation. Our findings identify a new, non-turbulent arena for dissipation anomaly and establish the interplay between thermal noise and nonequilibrium driving as a fundamental route to singular behavior in hydrodynamics. |
| title | Dissipation anomaly in gradient-driven nonequilibrium steady states |
| topic | Statistical Mechanics Fluid Dynamics |
| url | https://arxiv.org/abs/2511.17851 |