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 experiments and used in Fig. 2 and 3 in the main paper, all data are three-column files featuring time (s), position (nm), and force (pN);

2) OpticalStretching.zip, containing data from Optical-tweezer experiments shown in Fig. 4a in the main paper, all data are two-column files featuring time (s) and position (nm) traces;

3) OpticalSensing.zip, containing data from Optical-tweezer experiments shown in Fig. 4b in the main paper, all data are one-column files featuring position (m) traces, sampling frequency 25kHz;

4) OpticalMicroscopy.rar, containing data from Optical-microscopy experiments shown in Fig. 4c in the main paper, all data are one column files featuring position (nm) traces, sampling frequency 2kHz.

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 healthy donor. The PBS solution contains 130 mM NaCl, 20 mM K/Na phosphate buffer, 10 mM glucose, and 1 mg/mL BSA. For the experiments, 4μL of blood was diluted in 1mL of PBS. The OT-stretching consists of three steps: 1) the RBC is nonspecifically attached to a bead that is captured in an optical trap of stiffness 56pN/μm while the RBC remains outside the optical trap; 2) the bead is brought to the tip of a micropipette where it remains immobilized while the RBC remains attached on the other side of the bead; 3) a second bead is captured by the optical trap and brought to the opposite end of the RBC to form a dumbbell configuration. All measurements were made at 40kHz with a data acquisition board (PXI-1033, National Instruments, Austin, TX). Bead-RBC contact areas (Fig. 4A) were estimated using a multiscale feature extractor based on a Gaussian pyramid representation of the raw image followed by a Laplacian reconstruction.

OT-sensing RBC experiments. Experiments have been performed as described previously (H. Turlier, et al., Nature Physics 12, 513 (2016)). RBCs were obtained from a healthy donor by finger pricking. After washing in PBS-based cell medium (CM), cells were biotinylated using a 0.5mM NHS-PEG3400-biotin (Nektar Therapeutics, San Carlos, CA) solution in CM. Streptavidin-coated, 3.28μm diameter polystyrene beads were incubated with the biotinylated RBC, and four beads were attached to the RBC using a time-shared optical tweezers system. For the OT-sensing, three of the four beads were trapped (trap stiffness: 1.2pN/μm), and the cell and bead system was moved 20μm away from
the surface to avoid any unspecific substrate interaction. To detect the free fluctuations of the fourth bead (probe bead), the laser power on this bead was reduced to 0.1 mW which is insufficient to trap the bead (trap stiffness < 24fN/μm). The particle motion was recorded using a position-sensitive detector (PSD) placed in a plane conjugate to the back focal plane of the lightcollecting objective (Obj2 in Fig.4B). Low-frequency noise peaks known to originate from the stage were filtered in Fourier space. For OT-sensing, bead-RBC contact areas were estimated as described in H. Turlier, et al., Nature Physics 12, 513 (2016).

OM RBC experiments. Human RBCs were extracted from the blood of healthy donors and then separated by centrifugation at 5000g for 10 min at 4ºC, rinsed with PBS, and, finally,
diluted (1:15) with PBS supplemented with 10 mM glucose, and 1 mg/mL bovine serum albumin (R. Rodriguez-Garcia, et al., Biophysical Journal 108, 2794 (2015)). High-resolution time-lapse Optical Microscopy (OM) was performed using a phase contrast inverted microscope (NikonEclipse2000Ti) armed with a 100 W TI-12 DH Pillar Illu-
minator, an LWD 0.52 collimator, and a 100x oil immersion objective (PlanApoVC, N.A. 1.4; Nikon). RBC flickering was captured at the equatorial plane with a FASTCAM SA3 camera (Photron), with an effective pixel size of 50x50 nm2. Movies were recorded for 10s, with a sampling frequency of 2000 frames per second (2kHz).