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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.24611 |
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| _version_ | 1866913003773886464 |
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| author | Kooshkbaghi, Mahdi |
| author_facet | Kooshkbaghi, Mahdi |
| contents | Far-from-equilibrium kinetic systems collapse onto a hydrodynamic attractor, traditionally approximated by a gradient expansion. While temporal gradient series are non-Borel summable and require transseries completions, the analytic structure of the spatial expansion has remained elusive. Here, we derive exact closed-form Chapman--Enskog coefficients at all orders via Lagrange inversion and prove that the non-relativistic spatial gradient series, though factorially divergent, is strictly Borel summable. Furthermore, we show that this divergence originates from unbounded Galilean velocities; enforcing relativistic causality yields a convergent spatial hydrodynamic expansion with finite radius. Together with prior temporal results, our findings suggest that the hydrodynamic gradient expansion is always Borel summable, pointing to a non-perturbative route from kinetic theory to hydrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24611 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Spatial Hydrodynamic Attractor: Resurgence of the Gradient Expansion Kooshkbaghi, Mahdi Mathematical Physics High Energy Physics - Theory Far-from-equilibrium kinetic systems collapse onto a hydrodynamic attractor, traditionally approximated by a gradient expansion. While temporal gradient series are non-Borel summable and require transseries completions, the analytic structure of the spatial expansion has remained elusive. Here, we derive exact closed-form Chapman--Enskog coefficients at all orders via Lagrange inversion and prove that the non-relativistic spatial gradient series, though factorially divergent, is strictly Borel summable. Furthermore, we show that this divergence originates from unbounded Galilean velocities; enforcing relativistic causality yields a convergent spatial hydrodynamic expansion with finite radius. Together with prior temporal results, our findings suggest that the hydrodynamic gradient expansion is always Borel summable, pointing to a non-perturbative route from kinetic theory to hydrodynamics. |
| title | The Spatial Hydrodynamic Attractor: Resurgence of the Gradient Expansion |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.24611 |