Green-Kubo relations

Green-Kubo relations connect how a system's microscopic fluctuations relate to its macroscopic transport properties, like electrical conductivity or thermal conductivity. They show that the way particles or energy randomly fluctuate over time can be mathematically linked to the average flow or transfer of those quantities when a small external force or gradient is applied. Essentially, by studying the natural, spontaneous fluctuations within a system at equilibrium, scientists can predict how the system will respond to forces, providing a fundamental bridge between microscopic behavior and observable bulk properties.