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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.16247 |
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| _version_ | 1866916016384114688 |
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| author | Boynewicz, Jason Thumann, Michael C. Procopio, Giuseppe Giona, Massimiliano |
| author_facet | Boynewicz, Jason Thumann, Michael C. Procopio, Giuseppe Giona, Massimiliano |
| contents | Owing to the Chapman-Kolmogorov equation for Markovian dynamics,any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states. This property permits the unraveling of fine details of fluid-particle interactions at microscales defined by its non-equilibrium properties from the analysis of a single Brownian trajectory and to connect them to the hydrodynamics of the solvent fluid, simply considering the lower-order (second) moments of particle position in trapped conditions. In this way, the acceleration due to thermal-hydrodynamic fluctuational forces is isolated from the other factors and the short-time displacement statistics is completely determined by the correlation properties of the fluctuational thermal-hydrodynamic force. This approach not only confirms the $t^{5/2}$-law obtained by Boynewicz et al. (2026), related to fluid inertial effects, but indicates that this scaling may be superseded by a $t^4$-scaling at very short times once the correlated nature of the stochastic forcings is taken into account. The latter result is related to the regularity properties of particle velocity realizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Brownian motion: non-equilibrium states from equilibrium trajectories -- recovering hydrodynamic regimes from prepared displacement measurements Boynewicz, Jason Thumann, Michael C. Procopio, Giuseppe Giona, Massimiliano Statistical Mechanics Owing to the Chapman-Kolmogorov equation for Markovian dynamics,any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states. This property permits the unraveling of fine details of fluid-particle interactions at microscales defined by its non-equilibrium properties from the analysis of a single Brownian trajectory and to connect them to the hydrodynamics of the solvent fluid, simply considering the lower-order (second) moments of particle position in trapped conditions. In this way, the acceleration due to thermal-hydrodynamic fluctuational forces is isolated from the other factors and the short-time displacement statistics is completely determined by the correlation properties of the fluctuational thermal-hydrodynamic force. This approach not only confirms the $t^{5/2}$-law obtained by Boynewicz et al. (2026), related to fluid inertial effects, but indicates that this scaling may be superseded by a $t^4$-scaling at very short times once the correlated nature of the stochastic forcings is taken into account. The latter result is related to the regularity properties of particle velocity realizations. |
| title | Brownian motion: non-equilibrium states from equilibrium trajectories -- recovering hydrodynamic regimes from prepared displacement measurements |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2605.16247 |