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

Lapolla, Alessio; Hartich, David; Godec, Aljaž

doi:10.1103/physrevresearch.2.043084

Cited by 34 publications

(40 citation statements)

References 78 publications

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“…The fourth, time-average observable is a functional of the projected path l τ evolving from l τ =0 called the fraction of occupation time or "empirical density" [42]…”

Section: Conformational Dynamicsmentioning

confidence: 99%

Time- and ensemble-average statistical mechanics of the Gaussian network model

Lapolla

Vossel

Godec

2021

J. Phys. A: Math. Theor.

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We present analytical results for a set of time- and ensemble-averaged physical observables in the non-Hookean Gaussian network model (GNM)—a generalization of the Rouse model to elastic networks with links that display a certain degree of extensional and rotational stiffness. We focus on a set of coarse-grained observables that may be of interest in the analysis of GNM in the context of internal motions in proteins and mechanical frames in contact with a heat bath. A C++ computer code is made available that implements all analytical results.

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“…The fourth, time-average observable is a functional of the projected path l τ evolving from l τ =0 called the fraction of occupation time or "empirical density" [42]…”

Section: Conformational Dynamicsmentioning

confidence: 99%

Time- and ensemble-average statistical mechanics of the Gaussian network model

Lapolla

Vossel

Godec

2021

J. Phys. A: Math. Theor.

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“…with D, D ∈ [λ min , λ max ] bounded by the eigenvalues of D, and K, K are constants depending on the specific normalized window U z (see [89]). Moreover, taking U x (z) → δ(x − z) as in [7,51,[61][62][63][64][65][66][67][68] we find for d ≥ 2 that var x ρ,J (t), C xx Jρ (t) diverge for all t (see example in Fig. 3c).…”

mentioning

confidence: 96%

“…Such systems are typically small and "soft", and thus subject to large thermal fluctuations. Single-molecule experiments [45][46][47][48][49] probe non-equilibrium processes on the level of individual finite trajectories that are typically analyzed within the framework of "time-average statistical mechanics" [50,51] -by averaging along individual realizations yielding random quantities with nontrivial statistics.…”

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confidence: 99%

“…Moreover, current fluctuations have a noise floor -they are bounded from below by the "thermodynamic uncertainty relation" [31,34,76,77]. It is thus imperative to understand and control fluctuations of time-averaged observables [51].…”

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confidence: 99%

“…which allow us to write the exact two-point correlation of the empirical density in the form (see [89] and [51,53])…”

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confidence: 99%

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Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space

Dieball¹,

Godec²

2021

Preprint

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We present general results on fluctuations and spatial correlations of the empirical density and current of Markovian diffusion in an equilibrium or non-equilibrium steady state on all time scales. We unravel a deep connection between the kinematics of empirical current and "dual-reversal" symmetry. We highlight the essential rôle of coarse-graining in space -the fluctuations of empirical density and current defined in a point are insensitive to non-conservative forces, and are proven to diverge on all time scales in dimensions higher than one, implying non-Gaussian statistics. A spatial coarse-graining is required to uncover salient features of currents due to non-conservative forces. We apply the results to minimal two-dimensional examples of irreversible diffusion. Our findings provide a deeper understanding of time-averaged observables and may allow for a more reliable analysis of single-molecule and particle-tracking experiments.

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Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories

et al. 2021

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Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses spread or drugs may be delivered in biological cells. Similar time-series are being recorded of stock values in financial markets and of climate data. Such time-series are most typically evaluated in terms of time-averaged mean-squared displacements (TAMSDs), which remain random variables for finite measurement times. Their statistical properties are different for different physical stochastic processes, thus allowing us to extract valuable information on the stochastic process itself. To exploit the full potential of the statistical information encoded in measured time-series we here propose an easy-to-implement and computationally inexpensive new methodology, based on deviations of the TAMSD from its ensemble average counterpart. Specifically, we use the upper bound of these deviations for Brownian motion (BM) to check the applicability of this approach to simulated and real data sets. By comparing the probability of deviations for different data sets, we demonstrate how the theoretical bound for BM reveals additional information about observed stochastic processes. We apply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracer beads measured in mucin hydrogels, and of geographic surface temperature anomalies. Our analysis shows how the large-deviation properties can be efficiently used as a simple yet effective routine test to reject the BM hypothesis and unveil relevant information on statistical properties such as ergodicity breaking and short-time correlations.

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

Cited by 34 publications

References 78 publications

Time- and ensemble-average statistical mechanics of the Gaussian network model

Time- and ensemble-average statistical mechanics of the Gaussian network model

Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space

Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories

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