Toolbox for quantifying memory in dynamics along reaction coordinates

Lapolla, Alessio; Godec, Aljaž

doi:10.1103/physrevresearch.3.l022018

Cited by 18 publications

(10 citation statements)

References 60 publications

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“…Markovianity is an important characteristic of stochastic processes, and different methods to test for it are currently under debate (see e.g. [76,99,100]). For the important class of stochastic oscillators, computing the statistics of Q * 1 (x(t)), and specifically probing for a purely Lorentzian line shape, may provide another independent tool to test for Markovianity.…”

Section: Summary and Discussionmentioning

confidence: 99%

A Universal Description of Stochastic Oscillators

Pérez-Cervera¹,

Gutkin²,

Thomas³

et al. 2023

Preprint

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Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here we introduce a nonlinear transformation of stochastic oscillators to a new complex-valued function Q * 1 (x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function Q * 1 (x) is the eigenfunction of the Kolmogorov backward operator with the least negative (but non-vanishing) eigenvalue λ1 = µ1 + iω1. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency ω1 and half-width µ1; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around ω1; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.

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Section: Summary and Discussionmentioning

confidence: 99%

A Universal Description of Stochastic Oscillators

Pérez-Cervera¹,

Gutkin²,

Thomas³

et al. 2023

Preprint

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“…However, as soon as slow hidden degrees of freedom emerge (within A or B) the exact connection between the observed kinetics and the dissipation embodied in Eq. (1) disappears, which was explained theoretically [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and corroborated experimentally [29]. The equality (1) can nevertheless be restored under specific conditions [13,[30][31][32], using affinities [33], by stalling the system [34,35] or introducing waiting time distributions [27,[36][37][38] that inter alia can further trigger anomalous diffusion [39].…”

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confidence: 85%

Violation of Local Detailed Balance Despite a Clear Time-Scale Separation

Hartich¹,

Godec²

2021

Preprint

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Integrating out fast degrees of freedom is known to yield, to a good approximation, memory-less, i.e. Markovian, dynamics. In the presence of such a time-scale separation local detailed balance is believed to emerge and to guarantee thermodynamic consistency arbitrarily far from equilibrium.Here we present a transparent example of a Markov model of a molecular motor where local detailed balance can be violated despite a clear time-scale separation and hence Markovian dynamics. Driving the system far from equilibrium can lead to a violation of local detailed balance against the driving force. We further show that local detailed balance can be restored, even in the presence of memory, if the coarse-graining is carried out as Milestoning. Our work establishes Milestoning not only as a kinetically but for the first time also as a thermodynamically consistent coarse-graining method. Our results are relevant as soon as individual transition paths are appreciable or can be resolved.

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“…A solution, on the experimental side, is a development of multidimensional techniques. ,− On the data analysis side, irreversibility is often encoded in non-Markov effects. Such effects, fundamentally, cannot be neglected, and they can be detected with appropriate data analysis. , If discovering and quantifying the directionality of the observed dynamics are the objectives, it may also be desirable to estimate entropy production (eq ) directly from raw experimental time series (e.g., the photon sequence in Figure ) rather than after postprocessing the data using, e.g., hidden Markov models. In this regard, histogram entropy estimators and compression algorithm-based estimators appear to be promising, ,, although, to the best of our knowledge, they have not yet been applied to photon sequences.…”

Section: Summary and Future Directionsmentioning

confidence: 99%

Challenges in Inferring the Directionality of Active Molecular Processes from Single-Molecule Fluorescence Resonance Energy Transfer Trajectories

Godec¹,

Makarov

2022

J. Phys. Chem. Lett.

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We discuss some of the practical challenges that one faces in using stochastic thermodynamics to infer directionality of molecular machines from experimental single-molecule trajectories. Because of the limited spatiotemporal resolution of single-molecule experiments and because both forward and backward transitions between the same pairs of states cannot always be detected, differentiating between the forward and backward directions of, e.g., an ATP-consuming molecular machine that operates periodically, turns out to be a nontrivial task. Using a simple extension of a Markov-state model that is commonly employed to analyze single-molecule transition-path measurements, we illustrate how irreversibility can be hidden from such measurements but in some cases can be uncovered when non-Markov effects in low-dimensional single-molecule trajectories are considered.

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Toolbox for quantifying memory in dynamics along reaction coordinates

Cited by 18 publications

References 60 publications

A Universal Description of Stochastic Oscillators

A Universal Description of Stochastic Oscillators

Violation of Local Detailed Balance Despite a Clear Time-Scale Separation

Challenges in Inferring the Directionality of Active Molecular Processes from Single-Molecule Fluorescence Resonance Energy Transfer Trajectories

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