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  Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems

Lapolla, A., Hartich, D., & Godec, A. (2020). Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems. Physical Review Research, 2(4): 043084. doi:10.1103/PhysRevResearch.2.043084.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0007-4C75-1 Version Permalink: http://hdl.handle.net/21.11116/0000-0007-4C7B-B
Genre: Journal Article

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Lapolla, A.1, Author              
Hartich, D.2, Author              
Godec, A.1, Author              
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1Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_2396692              
2Department of Theoretical and Computational Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_578631              

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 Abstract: We present a spectral-theoretic approach to time-average statistical mechanics for general, nonequilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic stochastic dynamics with continuous or discrete state-space. We derive exact results for the mean, fluctuations, and correlations of time-average observables from the eigenspectrum of the underlying generator of Fokker-Planck or master equation dynamics, and we discuss the results from a physical perspective. Feynman-Kac formulas are rederived using Itô calculus and combined with non-Hermitian perturbation theory. The emergence of the universal central limit law in a spectral representation is shown explicitly on large-deviation timescales. For reversible dynamics with equilibrated initial conditions, we derive a general upper bound to fluctuations of occupation measures in terms of an integral of the return probability. Simple, exactly solvable examples are analyzed to demonstrate how to apply the theory. As a biophysical example, we revisit the Berg-Purcell problem on the precision of concentration measurements by a single receptor. Our results are directly applicable to a diverse range of phenomena underpinned by time-average observables and additive functionals in physical, chemical, biological, and economical systems.

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Language(s): eng - English
 Dates: 2020-10-152020-12
 Publication Status: Published in print
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 Rev. Type: Peer
 Identifiers: DOI: 10.1103/PhysRevResearch.2.043084
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Title: Physical Review Research
Source Genre: Journal
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Pages: 17 Volume / Issue: 2 (4) Sequence Number: 043084 Start / End Page: - Identifier: -