Variance sum rule for entropy production

Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule for displacement and force variances that permits us to measure the entropy production rate in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. Data for this analysis can be found in the repository (1) described below.  We then apply the variance sum rule to flickering experiments in human red blood cells (repositories (2-4)). We find that the entropy production rate is spatially heterogeneous with a finite correlation length (in particular, data in the repository (4)) and its average value agrees with calorimetry measurements. 
The dataset is composed of 4 repositories:
1) SwitchingTrap.zip, containing data from Optical-tweezer experi..., Optical trap experiments with beads. Experiments with colloidal particles (Figs.1,2) were done in a miniaturized version of an optical tweezers instrument described in Dieterich, J. Camunas-Soler, M. Ribezzi-Crivellari, U. Seifert, F. Ritort, Nature Physics11, 971 (2015). Measurements in Figures 1 and 2 were performed with highly stable miniaturized laser tweezers in the dual-trap mode. The instrument directly measures forces by linear momentum conservation. In all experiments, we used polystyrene calibration beads of 3μm diameter. Piezo actuators bend the optical fibers and allow us to move the trap while measuring the trap position using a light lever that deflects a fraction of the laser beam to a position-sensitive detector (PSD). Force and trap position measurements are acquired at 100 kHz bandwidth using a data acquisition board (PXI-1033, National Instruments, Austin, TX). 
OT-stretching RBC experiments. For the RBC experiments, human RBCs were obtained by finger pricking of a he..., , # Variance sum rule for entropy production

This dataset contains the data used for the analysis presented in the paper \"Variance sum rule for entropy production\". The dataset contains 4 repositories, each of these relative to a different experiment. Furthermore, we also include software in the form of a Jupyter Notebook to perform the Analysis described in the paper.

## Description of the data and file structure

The dataset contains 4 repositories.

1\) SwitchingTrap.zip, containing data of a Brownian particle trapped with optical tweezers and whose center jumps between two values at random times. The latter dynamics is governed by a two-state Master equation. The results of the analysis of this data is presented in Fig. 2 and 3 in the main paper.

The repository contains three repositories called \"18nm\", \"70nm\", \"280nm\", one for each experiment. The titles of the repositories refer to the distance between the minima between which the center of the optical tweezer is switching. Each...