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Abstract We propose and investigate a method for identifying timescales of dissipation in nonequilibrium steady states modeled as discrete-state Markov jump processes. The method is based on how the irreversibility—measured by the statistical breaking of time-reversal symmetry—varies under temporal coarse-graining. We observe a sigmoidal-like shape of the irreversibility as a function of the coarse-graining time whose functional form we derive for systems with a fast driven transition. This theoretical prediction allows us to develop a method for estimating the dissipative time scale from time-series data by fitting estimates of the irreversibility to our predicted functional form. We further analyze the accuracy and statistical fluctuations of this estimate.
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Aggregation Methods for Computing Steady States in Statistical Physics
We give a new proof of local convergence of a multigrid method called iterative aggregation/disaggregation (IAD) for computing steady states of Markov chains. Our proof leads naturally to precise and interpretable estimates of the asymptotic rate of convergence. We study IAD as a model of more complex methods from statistical physics for computing nonequilibrium steady states, such as the nonequilibrium umbrella sampling method of Warmflash, Bhimalapuram, and Dinner [J. Chem. Phys., 127 (2007), 154112]. We explain why it may be possible to use methods like IAD to efficiently calculate steady states of processes in statistical physics and how to choose parameters to optimize efficiency.
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- Award ID(s):
- 2012207
- PAR ID:
- 10471635
- Publisher / Repository:
- Society for Industial and Applied Mathematics
- Date Published:
- Journal Name:
- Multiscale Modeling & Simulation
- Volume:
- 21
- Issue:
- 3
- ISSN:
- 1540-3459
- Page Range / eLocation ID:
- 1170 to 1209
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1137/22M1530628
