Fluctuation-dissipation theorem

The fluctuation-dissipation theorem explains how tiny random motions in a system, like molecules jiggling in a fluid, are related to how the system responds when disturbed. Essentially, it states that the natural, spontaneous fluctuations provide information about how the system dissipates energy when acted upon. For example, the way a material heats up when shaken is connected to how its particles move randomly when at rest. This principle links microscopic random behavior to macroscopic responses, allowing scientists to predict how systems behave far from equilibrium based on their inherent fluctuations.