Least-rattling feedback from strong time-scale separation
In most interacting many-body systems associated with some “emergent phenomena,” we can identify subgroups of degrees of freedom that relax on dramatically different time scales. Time-scale separation of this kind is particularly helpful in nonequilibrium systems where only the fast variables are su...
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| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/114441 https://orcid.org/0000-0001-6850-5994 https://orcid.org/0000-0001-8414-3153 |
| _version_ | 1811085374003347456 |
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| author | Chvykov, Pavel England, Jeremy L. |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Chvykov, Pavel England, Jeremy L. |
| author_sort | Chvykov, Pavel |
| collection | MIT |
| description | In most interacting many-body systems associated with some “emergent phenomena,” we can identify subgroups of degrees of freedom that relax on dramatically different time scales. Time-scale separation of this kind is particularly helpful in nonequilibrium systems where only the fast variables are subjected to external driving; in such a case, it may be shown through elimination of fast variables that the slow coordinates effectively experience a thermal bath of spatially varying temperature. In this paper, we investigate how such a temperature landscape arises according to how the slow variables affect the character of the driven quasisteady state reached by the fast variables. Brownian motion in the presence of spatial temperature gradients is known to lead to the accumulation of probability density in low-temperature regions. Here, we focus on the implications of attraction to low effective temperature for the long-term evolution of slow variables. After quantitatively deriving the temperature landscape for a general class of overdamped systems using a path-integral technique, we then illustrate in a simple dynamical system how the attraction to low effective temperature has a fine-tuning effect on the slow variable, selecting configurations that bring about exceptionally low force fluctuation in the fast-variable steady state. We furthermore demonstrate that a particularly strong effect of this kind can take place when the slow variable is tuned to bring about orderly, integrable motion in the fast dynamics that avoids thermalizing energy absorbed from the drive. We thus point to a potentially general feedback mechanism in multi-time-scale active systems, that leads to the exploration of slow variable space, as if in search of fine tuning for a “least-rattling” response in the fast coordinates. |
| first_indexed | 2024-09-23T13:08:34Z |
| format | Article |
| id | mit-1721.1/114441 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:08:34Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1144412022-09-28T12:12:44Z Least-rattling feedback from strong time-scale separation Chvykov, Pavel England, Jeremy L. Massachusetts Institute of Technology. Department of Physics Chvykov, Pavel England, Jeremy L. In most interacting many-body systems associated with some “emergent phenomena,” we can identify subgroups of degrees of freedom that relax on dramatically different time scales. Time-scale separation of this kind is particularly helpful in nonequilibrium systems where only the fast variables are subjected to external driving; in such a case, it may be shown through elimination of fast variables that the slow coordinates effectively experience a thermal bath of spatially varying temperature. In this paper, we investigate how such a temperature landscape arises according to how the slow variables affect the character of the driven quasisteady state reached by the fast variables. Brownian motion in the presence of spatial temperature gradients is known to lead to the accumulation of probability density in low-temperature regions. Here, we focus on the implications of attraction to low effective temperature for the long-term evolution of slow variables. After quantitatively deriving the temperature landscape for a general class of overdamped systems using a path-integral technique, we then illustrate in a simple dynamical system how the attraction to low effective temperature has a fine-tuning effect on the slow variable, selecting configurations that bring about exceptionally low force fluctuation in the fast-variable steady state. We furthermore demonstrate that a particularly strong effect of this kind can take place when the slow variable is tuned to bring about orderly, integrable motion in the fast dynamics that avoids thermalizing energy absorbed from the drive. We thus point to a potentially general feedback mechanism in multi-time-scale active systems, that leads to the exploration of slow variable space, as if in search of fine tuning for a “least-rattling” response in the fast coordinates. Gordon and Betty Moore Foundation (Grant GBMF4343) 2018-03-29T15:12:21Z 2018-03-29T15:12:21Z 2018-03 2018-01 2018-03-15T18:00:27Z Article http://purl.org/eprint/type/JournalArticle 2470-0045 2470-0053 http://hdl.handle.net/1721.1/114441 Chvykov, Pavel, and Jeremy England. “Least-Rattling Feedback from Strong Time-Scale Separation.” Physical Review E, vol. 97, no. 3, Mar. 2018. © 2018 American Physical Society https://orcid.org/0000-0001-6850-5994 https://orcid.org/0000-0001-8414-3153 en http://dx.doi.org/10.1103/PhysRevE.97.032115 Physical Review E Creative Commons Attribution http://creativecommons.org/licenses/by/3.0 application/pdf American Physical Society American Physical Society |
| spellingShingle | Chvykov, Pavel England, Jeremy L. Least-rattling feedback from strong time-scale separation |
| title | Least-rattling feedback from strong time-scale separation |
| title_full | Least-rattling feedback from strong time-scale separation |
| title_fullStr | Least-rattling feedback from strong time-scale separation |
| title_full_unstemmed | Least-rattling feedback from strong time-scale separation |
| title_short | Least-rattling feedback from strong time-scale separation |
| title_sort | least rattling feedback from strong time scale separation |
| url | http://hdl.handle.net/1721.1/114441 https://orcid.org/0000-0001-6850-5994 https://orcid.org/0000-0001-8414-3153 |
| work_keys_str_mv | AT chvykovpavel leastrattlingfeedbackfromstrongtimescaleseparation AT englandjeremyl leastrattlingfeedbackfromstrongtimescaleseparation |