Fluctuation-Dissipation Relations

The fluctuation-dissipation relation (FDT), predicted by Onsager in 1931, is a fundamental cornerstone of statistical physics. Generally true only close to thermal equilibrium, it reveals that the reaction of a system to a small external perturbation and the decay of an internal fluctuation created by thermal noise are indistinguishable. The connection between diffusion coefficient and mobility, known as Stokes-Einstein relation, is certainly the most prominent example.

Violations of the FDT are a clear fingerprint of a nonequilibrium system. Recent theoretical developments derived different variants of a generalized FDT for a specific class of nonequilibrium systems, i.e. nonequilibrium steady states (NESSs). In such a NESS, detailed balance is broken, while the system is still characterized by a stationary probability distribution. 

To experimentally study the generalized FDT, we use a Brownian particle periodically driven between two slightly different NESSs. Our measurements confirm the validity of the generalized FDT for two different variants. Furthermore, we demonstrate that although both are equivalent from a theoretical point of view, large differences regarding the size of experimental errors exist. Therefore, the right choice of variant is important for the accurate determination of the response in such measurements.