Non-equilibrium steady states (NESS) pervade nature, from climate dynamics on the planetary scale to the activity of living cells at the molecular level. Key to NESS is the entropy production rate σ at which energy is dissipated to the environment. Despite its importance, σ remains challenging to measure, especially in nanoscale systems where one has limited access to microscopic variables. We introduce a variance sum rule (VSR) for the displacement and the cumulative force in a NESS that permits us to derive σ from positions and forces trajectories. When all degrees of freedom are (experimentally) accessible, this estimation can be performed from short time measurements. We apply this method both from an analytical and experimental point of view, showing its robustness and usefulness in many practical situations. If all degrees of freedom are not experimentally accessible, then one can resort to a model dependent fitting procedure based on the VSR, that is more reliable and robust than the usual fits based on correlation functions. In particular, this methodology is applied to mechanically stretched red blood cells for the estimation of σ associated to membrane flickering. The variance sum rule sets a new resource for exploiting fluctuations to measure physical quantities in non-equilibrium stochastic systems.
Marco Baiesi
