Thermodynamic uncertainty relations in the presence of non-linear friction and memory
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| Format: | Preprint |
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2023
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| _version_ | 1866913344475103232 |
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| author | Plati, A. Puglisi, A. Sarracino, A. |
| author_facet | Plati, A. Puglisi, A. Sarracino, A. |
| contents | A new Thermodynamic Uncertainty Relation (TUR) is derived for systems described by linearly coupled Langevin equations in the presence of non-linear frictional forces. In our scheme, the main variable represents the velocity of a particle, while the other coupled variables describe memory effects which may arise from strongly correlated degrees of freedom with several time-scales and, in general, are associated with thermal baths at different temperatures. The new TUR gives a lower bound for the mean-squared displacement of the position of the particle, including its asymptotic diffusion coefficient. This bound, in several examples worked out here, appears to be a good analytical estimate of the real diffusion coefficient. The new TUR can be also applied in the absence of any external force (with or without thermal equilibrium between the baths), a case which usually goes beyond the scope of original TURs. We show applications to non-linear frictional models with memory, such as the Coulomb and the Prantdtl-Tomlinson models, usually representative of friction at the nano-scale and within atomic-force microscopy experiments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_15243 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Thermodynamic uncertainty relations in the presence of non-linear friction and memory Plati, A. Puglisi, A. Sarracino, A. Statistical Mechanics Soft Condensed Matter A new Thermodynamic Uncertainty Relation (TUR) is derived for systems described by linearly coupled Langevin equations in the presence of non-linear frictional forces. In our scheme, the main variable represents the velocity of a particle, while the other coupled variables describe memory effects which may arise from strongly correlated degrees of freedom with several time-scales and, in general, are associated with thermal baths at different temperatures. The new TUR gives a lower bound for the mean-squared displacement of the position of the particle, including its asymptotic diffusion coefficient. This bound, in several examples worked out here, appears to be a good analytical estimate of the real diffusion coefficient. The new TUR can be also applied in the absence of any external force (with or without thermal equilibrium between the baths), a case which usually goes beyond the scope of original TURs. We show applications to non-linear frictional models with memory, such as the Coulomb and the Prantdtl-Tomlinson models, usually representative of friction at the nano-scale and within atomic-force microscopy experiments. |
| title | Thermodynamic uncertainty relations in the presence of non-linear friction and memory |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2312.15243 |