Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics

Abstract

Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare the performance of three different entropy estimators under these limitations for two different paradigmatic systems, a four-state Markov network and an augmented Michaelis-Menten reaction scheme. We consider the thermodynamic uncertainty relation, a waiting-time based estimator for resolved transitions and a waiting-time based estimator for blurred transitions in imperfect observation scenarios. For perfect measurement statistics and finite temporal resolution, the estimator based on resolved transitions performs best in all considered scenarios. The thermodynamic uncertainty relation gives a better estimate than the estimator based on blurred transitions at low driving affinities, whereas the latter performs better at high driving affinities. Furthermore, we find that a higher temporal and spatial resolution leads to slower convergence of measurement statistics, implying that for short measurement times, a lower resolution may be beneficial. Additionally, we identify a self-averaging effect for the waiting-time based entropy estimators that can reduce their variance for observations with finite statistics.

References in corpus (57)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Thermodynamic uncertainty relation for biomolecular processes
• Dissipation bounds all steady-state current fluctuations
• Stochastic thermodynamics under coarse-graining
• Single-molecule experiments in biological physics: methods and applications
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Universal bounds on current fluctuations
• Estimating dissipation from single stationary trajectories
• Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics
• Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist's perspective
• Stochastic thermodynamics of chemical reaction networks
• Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems
• Multidimensional thermodynamic uncertainty relations
• Fluctuation Theorem for Partially-masked Nonequilibrium Dynamics
• Lower bounds on dissipation upon coarse graining
• Uncertainty relations in stochastic processes: An information inequality approach
• Inferring broken detailed balance in the absence of observable currents
• Stochastic thermodynamics of single enzymes and molecular motors
• Improved bounds on entropy production in living systems
• Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
• Effective thermodynamics for a marginal observer
• Multiple-scale stochastic processes: decimation, averaging and beyond
• Universal Bound on the Fano Factor in Enzyme Kinetics
• Entropy production and coarse-graining in Markov processes
• Fluctuation relations and coarse-graining
• Hierarchical Bounds on Entropy Production Inferred from Partial Information
• Fluctuation Theorem for Hidden Entropy Production
• Variance Sum Rule for Entropy Production
• Emergent memory and kinetic hysteresis in strongly driven networks
• Continuous time random walk for open systems: Fluctuation theorems and counting statistics
• Thermodynamic Bound on the Asymmetry of Cross-Correlations
• Exact Coarse Graining Preserves Entropy Production out of Equilibrium
• Thermodynamically Consistent Coarse Graining of Biocatalysts beyond Michaelis--Menten
• Coarse graining of master equations with fast and slow states
• Second law of thermodynamics at stopping times
• Dynamical fluctuations for semi-Markov processes
• Time-resolved statistics of snippets as general framework for model-free entropy estimators
• Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
• Inference in non-equilibrium systems from incomplete information: the case of linear systems and its pitfalls
• Tightest bound on hidden entropy production from partially observed dynamics
• Violation of Local Detailed Balance Despite a Clear Time-Scale Separation
• Estimating Entropy Production Rates with First-Passage Processes
• Fluctuations of Apparent Entropy Production in Networks with Hidden Slow Degrees of Freedom
• Thermodynamic cost for precision of general counting observables
• Operationally Accessible Uncertainty Relations for Thermodynamically Consistent Semi-Markov Processes
• Fluctuating Entropy Production on the Coarse-Grained Level: Inference and Localization of Irreversibility
• General theory for localizing the where and when of entropy production meets single-molecule experiments
• Reversal symmetries for cyclic paths away from thermodynamic equilibrium
• Effective estimation of entropy production with lacking data
• Cycle counts and affinities in stochastic models of non-equilibrium systems
• Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime
• An estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions
• Variance sum rule: proofs and solvable models
• Statistical features of systems driven by non-Gaussian processes: theory & practice
• Dissipation at limited resolutions: Power law and detection of hidden dissipative scales
• Waiting time distributions in hybrid models of motor-bead assays: A concept and tool for inference
• Multicyclic norias: a first-transition approach to extreme values of the currents

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