Variance Sum Rule for Entropy Production

Abstract

We introduce a variance sum rule for displacement and force variances that permits us to directly measure the entropy production rate σ in nonequilibrium steady states. We illustrate it for an active Brownian particle in an optical trap where σ varies over three decades 10−104kBT/s. We then apply the variance sum rule to human red blood cells in experiments with laser optical tweezers and ultrafast life-imaging microscopy. We find that σ is spatially heterogeneous with correlation length ξ=0.6(2)μm and heat flux density jσ∼104kBT/(s⋅μm2). Our estimate σRBC∼106kBT/s per single cell agrees with macroscopic calorimetry measurements. The variance sum rule sets a new resource for exploiting fluctuations to measure entropy production rates across scales in active and living matter.