Title: Variance sum rule for entropy production

Non-equilibrium steady states, from the planetary scale to biological processes, are characterized by entropy production via energy dissipation to the environment, which is often challenging to measure. We introduce a variance sum rule (VSR) for displacement and impulse variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. By further introducing a model-dependent fitting procedure, we develop a method based on the VSR to derive σ from one-dimensional stochastic traces without measuring forces. In particular, we apply this inference procedure to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements.