Fluctuation-response relation of many Brownian particles under nonequilibrium conditions

We study many interacting Brownian particles under a tilted periodic potential. We numerically measure the linear response coefficient of the density field by applying a slowly varying potential transversal to the tilted direction. In equilibrium cases, the linear response coefficient is related to the intensity of density fluctuations in a universal manner, which is called a fluctuation-response relation. We then report numerical evidence that this relation holds even in nonequilibrium cases. This result suggests that Einstein's formula on density fluctuations can be extended to driven diffusive systems when the slowly varying potential is applied in a direction transversal to the driving force.