Thermodynamic inference based on coarse-grained data or noisy measurements

Abstract

Fluctuation theorems have become an important tool in single molecule biophysics to measure free energy differences from non-equilibrium experiments. When significant coarse-graining or noise affect the measurements, the determination of the free energies becomes challenging. In order to address this thermodynamic inference problem, we propose improved estimators of free energy differences based on fluctuation theorems, which we test on a number of examples. The effect of the noise can be described by an effective temperature, which only depends on the signal to noise ratio, when the work is Gaussian distributed and uncorrelated with the error made on the work. The notion of effective temperature appears less useful for non-Gaussian work distributions or when the error is correlated with the work, but nevertheless, as we show, improved estimators can still be constructed for such cases. As an example of non-trivial correlations between the error and the work, we also consider measurements with delay, as described by linear Langevin equations.

19 pages, 8 figures. Submitted to Phys. Rev. E

References in corpus (9)

• Rare events and the convergence of exponentially averaged work values
• Fluctuation Theorem for Partially-masked Nonequilibrium Dynamics
• Second-law-like inequalities with information and their interpretations
• Entropy production and coarse-graining in Markov processes
• Fluctuation relations and coarse-graining
• Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle
• Unifying approach for fluctuation theorems from joint probability distributions
• Free energy inference from partial work measurements in small systems
• Energy versus information based estimations of dissipation using a pair of magnetic colloidal particles

Cited by in corpus (9)

• An operational approach to quantum stochastic thermodynamics
• Effective fluctuation and response theory
• Stochastic thermodynamics with arbitrary interventions
• Stochastic thermodynamics based on incomplete information: Generalized Jarzynski equality with measurement errors with or without feedback
• Hidden slow degrees of freedom and fluctuation theorems: an analytically solvable model
• Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter
• Coarse-grained Second Order Response Theory
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Convergence of thermodynamic quantities and work fluctuation theorems in presence of random protocols