In 1827, botanist Robert Brown observed the erratic movement of small particles in water. The statistical laws of what then became known as Brownian motion were later formulated by Albert Einstein, who explained the particles’ fluctuations in terms of the random forces  caused by collisions with the surrounding water molecules. Einstein’s work is considered a milestone of modern physics, as it not only  provided the theoretical foundation for the proof of the existence of atoms, but also established a connection between microscopic interactions and macroscopic dissipation: macroscopic objects experience friction because they lose momentum to the microscopic constituents of their environment. Today, Einstein’s relations and analogous results are called fluctuation-dissipation relations (FDRs) and can be employed to infer microscopic properties from macroscopic measurements. However, they are only valid for systems under equilibrium conditions, i.e., when there are no forces acting on the system and thus all currents vanish on average. This work shows that FDRs also apply to systems globally far from equilibrium. We considered fluctuations of a stalled, quiescent current in presence of other currents of arbitrary magnitude, showing that the FDR remains true under a certain condition regarding the coupling of the perturbing force to the microscopic mechanisms that contribute to the observable macroscopic effect. Moreover, we showed that in many modern experiments on small systems, like molecular motors or nanoscopic electronic devices, these conditions are indeed fulfilled. The new result thus extends the micro-macro connection to systems far from equilibrium and has potential applications for living systems.

We discuss these ideas in:

B. Altaner, MP, and M. Esposito, Fluctuation-Dissipation Relations Far from Equilibrium, Phys. Rev. Lett. 117, 180601 (2016), arXiv:1604.08832