title: 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 nonequilibrium 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 nontrivial correlations between the error and the work, we also consider measurements with delay, as described by linear Langevin equations.
authors.affiliation: Laboratoire de Physique et Mécanique des Milieux Hétérogènes-UMR CNRS 7636, ESPCI, 10 rue de Vauquelin, 75231 Paris cedex 05, France.
authors.forename: Reinaldo
authors.initials: R
authors.lastname: García-García
authors.affiliation: Laboratoire de Physico-Chimie Théorique-UMR CNRS Gulliver 7083, PSL Research University, ESPCI, 10 rue de Vauquelin, 75231 Paris cedex 05, France.
authors.forename: Sourabh
authors.initials: S
authors.lastname: Lahiri
authors.affiliation: Laboratoire de Physico-Chimie Théorique-UMR CNRS Gulliver 7083, PSL Research University, ESPCI, 10 rue de Vauquelin, 75231 Paris cedex 05, France.
authors.forename: David
authors.initials: D
authors.lastname: Lacoste