Coarse graining empirical densities and currents in continuous-space steady states
We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales—observables central to statistical mechanics and thermodynamics on the level of individ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.033243 |
| _version_ | 1797210651699970048 |
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| author | Cai Dieball Aljaž Godec |
| author_facet | Cai Dieball Aljaž Godec |
| author_sort | Cai Dieball |
| collection | DOAJ |
| description | We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales—observables central to statistical mechanics and thermodynamics on the level of individual trajectories. We focus on the important and nontrivial effect of a spatial coarse graining. Making use of a generalized time-reversal symmetry we provide deeper insight about the physical meaning of fluctuations of the coarse-grained empirical density and current, and explain why a systematic variation of the coarse-graining scale offers an efficient method to infer bounds on a system's dissipation. Moreover, we discuss emerging symmetries in the statistics of the empirical density and current, and the statistics in the central-limit regime. More broadly our work promotes the application of stochastic calculus as a powerful direct alternative to Feynman-Kac theory and path-integral methods. |
| first_indexed | 2024-04-24T10:13:59Z |
| format | Article |
| id | doaj.art-6e70de1b4f154ef2a7d0e6fafd37e2ac |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:13:59Z |
| publishDate | 2022-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-6e70de1b4f154ef2a7d0e6fafd37e2ac2024-04-12T17:24:51ZengAmerican Physical SocietyPhysical Review Research2643-15642022-09-014303324310.1103/PhysRevResearch.4.033243Coarse graining empirical densities and currents in continuous-space steady statesCai DieballAljaž GodecWe present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales—observables central to statistical mechanics and thermodynamics on the level of individual trajectories. We focus on the important and nontrivial effect of a spatial coarse graining. Making use of a generalized time-reversal symmetry we provide deeper insight about the physical meaning of fluctuations of the coarse-grained empirical density and current, and explain why a systematic variation of the coarse-graining scale offers an efficient method to infer bounds on a system's dissipation. Moreover, we discuss emerging symmetries in the statistics of the empirical density and current, and the statistics in the central-limit regime. More broadly our work promotes the application of stochastic calculus as a powerful direct alternative to Feynman-Kac theory and path-integral methods.http://doi.org/10.1103/PhysRevResearch.4.033243 |
| spellingShingle | Cai Dieball Aljaž Godec Coarse graining empirical densities and currents in continuous-space steady states Physical Review Research |
| title | Coarse graining empirical densities and currents in continuous-space steady states |
| title_full | Coarse graining empirical densities and currents in continuous-space steady states |
| title_fullStr | Coarse graining empirical densities and currents in continuous-space steady states |
| title_full_unstemmed | Coarse graining empirical densities and currents in continuous-space steady states |
| title_short | Coarse graining empirical densities and currents in continuous-space steady states |
| title_sort | coarse graining empirical densities and currents in continuous space steady states |
| url | http://doi.org/10.1103/PhysRevResearch.4.033243 |
| work_keys_str_mv | AT caidieball coarsegrainingempiricaldensitiesandcurrentsincontinuousspacesteadystates AT aljazgodec coarsegrainingempiricaldensitiesandcurrentsincontinuousspacesteadystates |