Chaos in Nonequilibrium Two-Temperature $(T_x, T_y)$ Nosé-Hoover Cell Models
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912568161861632 |
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| author | Arabzadeh, Hesam Hoover, Carol Griswold Hoover, William Graham Holian, Brad Lee |
| author_facet | Arabzadeh, Hesam Hoover, Carol Griswold Hoover, William Graham Holian, Brad Lee |
| contents | We revisit a two-temperature Nosé-Hoover wanderer particle embedded in a two-dimensional periodic 2x2 cell with four smooth repulsive corners at $(x,y) = (\pm 1, \pm 1)$ to explore chaos with anisotropic thermostatting. The model employs separate thermostats in the x and y directions, enabling controlled deviations from equilibrium. By integrating the full six-dimensional equations of motion and computing the complete Lyapunov spectrum, we confirm chaos and quantify phase-space contraction with high numerical precision. The total contraction rate, interpreted as entropy production, increases nonlinearly with the thermostat anisotropy, deviating from the quadratic dependence expected from linear-response theory, $Λ\propto -δ^{2}$. We compare two fits for $Λ$ as a function of $δ= 0.5 -T_y$: 1) a power law, $Λ\propto -δ^{2.44}$, 2) a quadratic-plus-quartic expansion. While the former captures low-driving behavior slightly better, the latter more accurately describes the strongly driven regime and remains consistent with linear response theory near equilibrium. An empirical linear relation between dissipation and phase-space dimensionality loss is also identified, $Λ\propto (D_{KY}-6) / 3$, where $D_{KY}$ is the approximate Kaplan-Yorke dimension. Our results demonstrate that nonlinear dissipation scaling emerges naturally even in minimal driven systems. Momentum statistics show significant non-Gaussian behavior under strong driving. Despite its dissipative nature, the model remains strictly time-reversible, offering a pedagogically rich example of microscopic reversibility coexisting with macroscopic entropy production. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chaos in Nonequilibrium Two-Temperature $(T_x, T_y)$ Nosé-Hoover Cell Models Arabzadeh, Hesam Hoover, Carol Griswold Hoover, William Graham Holian, Brad Lee Statistical Mechanics Chaotic Dynamics We revisit a two-temperature Nosé-Hoover wanderer particle embedded in a two-dimensional periodic 2x2 cell with four smooth repulsive corners at $(x,y) = (\pm 1, \pm 1)$ to explore chaos with anisotropic thermostatting. The model employs separate thermostats in the x and y directions, enabling controlled deviations from equilibrium. By integrating the full six-dimensional equations of motion and computing the complete Lyapunov spectrum, we confirm chaos and quantify phase-space contraction with high numerical precision. The total contraction rate, interpreted as entropy production, increases nonlinearly with the thermostat anisotropy, deviating from the quadratic dependence expected from linear-response theory, $Λ\propto -δ^{2}$. We compare two fits for $Λ$ as a function of $δ= 0.5 -T_y$: 1) a power law, $Λ\propto -δ^{2.44}$, 2) a quadratic-plus-quartic expansion. While the former captures low-driving behavior slightly better, the latter more accurately describes the strongly driven regime and remains consistent with linear response theory near equilibrium. An empirical linear relation between dissipation and phase-space dimensionality loss is also identified, $Λ\propto (D_{KY}-6) / 3$, where $D_{KY}$ is the approximate Kaplan-Yorke dimension. Our results demonstrate that nonlinear dissipation scaling emerges naturally even in minimal driven systems. Momentum statistics show significant non-Gaussian behavior under strong driving. Despite its dissipative nature, the model remains strictly time-reversible, offering a pedagogically rich example of microscopic reversibility coexisting with macroscopic entropy production. |
| title | Chaos in Nonequilibrium Two-Temperature $(T_x, T_y)$ Nosé-Hoover Cell Models |
| topic | Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2507.10863 |