Long-tailed dissipationless hydromechanics: weak thermalization and ergodicity breaking
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| Format: | Preprint |
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2025
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| _version_ | 1866908363600691200 |
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| author | Procopio, Giuseppe Pezzotti, Chiara Giona, Massimiliano |
| author_facet | Procopio, Giuseppe Pezzotti, Chiara Giona, Massimiliano |
| contents | We analyze the dynamic properties of dissipationless Generalized Langevin Equations in the presence of fluid inertial kernels possessing power-law tails, $k(t) \sim t^{-κ}$. While for $κ>1$ the dynamics is manifestly non ergodic, no thermalization occurs, and particle motion is ballistic, new phenomena arise for $0 < κ<1$. In this case, a form of weak thermalization appears in the presence of thermal/hydrodynamic fluctuations and attractive potentials. However, the absence of dissipation clearly emerges once an external constant force is applied: an asymptotic settling velocity cannot be achieved as the expected value of the particle velocity diverges. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_09566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-tailed dissipationless hydromechanics: weak thermalization and ergodicity breaking Procopio, Giuseppe Pezzotti, Chiara Giona, Massimiliano Statistical Mechanics We analyze the dynamic properties of dissipationless Generalized Langevin Equations in the presence of fluid inertial kernels possessing power-law tails, $k(t) \sim t^{-κ}$. While for $κ>1$ the dynamics is manifestly non ergodic, no thermalization occurs, and particle motion is ballistic, new phenomena arise for $0 < κ<1$. In this case, a form of weak thermalization appears in the presence of thermal/hydrodynamic fluctuations and attractive potentials. However, the absence of dissipation clearly emerges once an external constant force is applied: an asymptotic settling velocity cannot be achieved as the expected value of the particle velocity diverges. |
| title | Long-tailed dissipationless hydromechanics: weak thermalization and ergodicity breaking |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2505.09566 |