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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.08560 |
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| _version_ | 1866912614180716544 |
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| author | Grabsch, Aurélien Venturelli, Davide Bénichou, Olivier |
| author_facet | Grabsch, Aurélien Venturelli, Davide Bénichou, Olivier |
| contents | Characterising the statistical properties of classical interacting particle systems is a long-standing question. For Brownian particles the microscopic density obeys a stochastic evolution equation, known as the Dean--Kawasaki equation. This equation remains mostly formal and linearization (or higher-order expansions) is required to obtain explicit expressions for physical observables, with a range of validity not easily defined. Here, by combining macroscopic fluctuation theory with equilibrium statistical mechanics, we provide a systematic alternative to the Dean--Kawasaki framework to characterize large-scale correlations. This approach enables us to obtain explicit and exact results for dynamical observables such as tracer cumulants and bath-tracer correlations in one dimension, both in and out of equilibrium. In particular, we reveal a generic non-monotonic spatial structure in the response of the bath following a temperature quench. Our approach applies to a broad class of interaction potentials and extends naturally to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation Grabsch, Aurélien Venturelli, Davide Bénichou, Olivier Statistical Mechanics Characterising the statistical properties of classical interacting particle systems is a long-standing question. For Brownian particles the microscopic density obeys a stochastic evolution equation, known as the Dean--Kawasaki equation. This equation remains mostly formal and linearization (or higher-order expansions) is required to obtain explicit expressions for physical observables, with a range of validity not easily defined. Here, by combining macroscopic fluctuation theory with equilibrium statistical mechanics, we provide a systematic alternative to the Dean--Kawasaki framework to characterize large-scale correlations. This approach enables us to obtain explicit and exact results for dynamical observables such as tracer cumulants and bath-tracer correlations in one dimension, both in and out of equilibrium. In particular, we reveal a generic non-monotonic spatial structure in the response of the bath following a temperature quench. Our approach applies to a broad class of interaction potentials and extends naturally to higher dimensions. |
| title | Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2504.08560 |