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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2406.08885 |
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| _version_ | 1866911915921375232 |
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| author | Acharya, Subhajit Bagchi, Biman |
| author_facet | Acharya, Subhajit Bagchi, Biman |
| contents | Intermolecular correlations lower values of both diffusion and entropy. We present an analysis of the existing relations between long-time diffusion (D) and entropy. S. A recently proposed inequality, a lower bound, by Sorkin et al., expresses the long-time diffusion in terms of diffusion in a reference state and the entropy difference. Such a relationship may provide a measure of intermolecular correlations. We show that for a one-dimensional rugged energy landscape, the lower bound becomes equality only if certain three-site correlations are neglected. When these correlations are included, we can derive an accurate expression that agrees with computer simulations. The strong dimensionality dependence of diffusion of a Brownian particle in a rugged energy landscape also resembles the recently proposed inequality. We show that for interacting colloids, a mode-coupling theory-type calculation of diffusion coefficient can be combined with the new inequality to estimate entropy change from long-range inter-colloid correlations. Interestingly, the rate of barrier crossing in a multidimensional potential energy surface, related to diffusion in a periodic lattice, is shown to admit a relation that depends on the entropy change in a way reminiscent of the relation between D and S. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08885 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relation between Entropy, Diffusion and Relaxation Kinetics Acharya, Subhajit Bagchi, Biman Statistical Mechanics Intermolecular correlations lower values of both diffusion and entropy. We present an analysis of the existing relations between long-time diffusion (D) and entropy. S. A recently proposed inequality, a lower bound, by Sorkin et al., expresses the long-time diffusion in terms of diffusion in a reference state and the entropy difference. Such a relationship may provide a measure of intermolecular correlations. We show that for a one-dimensional rugged energy landscape, the lower bound becomes equality only if certain three-site correlations are neglected. When these correlations are included, we can derive an accurate expression that agrees with computer simulations. The strong dimensionality dependence of diffusion of a Brownian particle in a rugged energy landscape also resembles the recently proposed inequality. We show that for interacting colloids, a mode-coupling theory-type calculation of diffusion coefficient can be combined with the new inequality to estimate entropy change from long-range inter-colloid correlations. Interestingly, the rate of barrier crossing in a multidimensional potential energy surface, related to diffusion in a periodic lattice, is shown to admit a relation that depends on the entropy change in a way reminiscent of the relation between D and S. |
| title | Relation between Entropy, Diffusion and Relaxation Kinetics |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2406.08885 |