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 [1,2] that permits us to measure the entropy production rate σ in nonequilibrium steady states. We illustrate how this result allows the detection of non-equilibrium from kinetic measurements with and without force measurements. 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 for exact estimation of σ. In particular, we apply this inference procedure to flickering experiments in human red blood cells [1]. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements.
[1] I. Di Terlizzi et al., Science 383, 971–976 (2024)
[2] I. Di Terlizzi, M. Baiesi, F. Ritort, New J. Phys. 26, 063013 (2024)
