Statistical formulation of Onsager-Machlup variational principle
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914963144048640 |
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| author | Yasuda, Kento Ishimoto, Kenta Komura, Shigeyuki |
| author_facet | Yasuda, Kento Ishimoto, Kenta Komura, Shigeyuki |
| contents | Onsager's variational principle (OVP) provides us with a systematic way to derive dynamical equations for various soft matter and active matter. By reformulating the Onsager-Machlup variational principle (OMVP), which is a time-global principle, we propose a new method to incorporate thermal fluctuations. To demonstrate the utility of the statistical formulation of OMVP (SOMVP), we obtain the diffusion constant of a Brownian particle embedded in a viscous fluid only by maximizing the modified Onsager-Machlup integral for the surrounding fluid. We also apply our formulation to a Brownian particle in a steady shear flow, which is a typical example of a non-equilibrium system. Possible extensions of our formulation to internally driven active systems are discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_18611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Statistical formulation of Onsager-Machlup variational principle Yasuda, Kento Ishimoto, Kenta Komura, Shigeyuki Soft Condensed Matter Onsager's variational principle (OVP) provides us with a systematic way to derive dynamical equations for various soft matter and active matter. By reformulating the Onsager-Machlup variational principle (OMVP), which is a time-global principle, we propose a new method to incorporate thermal fluctuations. To demonstrate the utility of the statistical formulation of OMVP (SOMVP), we obtain the diffusion constant of a Brownian particle embedded in a viscous fluid only by maximizing the modified Onsager-Machlup integral for the surrounding fluid. We also apply our formulation to a Brownian particle in a steady shear flow, which is a typical example of a non-equilibrium system. Possible extensions of our formulation to internally driven active systems are discussed. |
| title | Statistical formulation of Onsager-Machlup variational principle |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2404.18611 |