Thermodynamic inference based on coarse-grained data or noisy measurements

TL;DR

This paper develops improved free energy estimators using fluctuation theorems for noisy or coarse-grained data, addressing challenges in thermodynamic inference from imperfect measurements in biophysics.

Contribution

It introduces new estimators that account for noise and coarse-graining, extending fluctuation theorem applications to more realistic experimental conditions.

Findings

Effective temperature depends on signal-to-noise ratio for Gaussian, uncorrelated work.

Improved estimators are effective even with non-Gaussian work distributions.

Estimators can handle correlated errors, such as measurements with delay.

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.