  The Green-Kubo relation, the Einstein relation, and the fluctuation-response
relation are representative universal relations among measurable quantities
that are valid in the linear response regime. We provide pedagogical proofs of
these universal relations for stochastic many-body systems. Through these
simple proofs, we characterize the three relations as follows. The Green-Kubo
relation is a direct result of the local detailed balance condition, the
fluctuation-response relation represents the dynamic extension of both the
Green-Kubo relation and the fluctuation relation in equilibrium statistical
mechanics, and the Einstein relation can be understood by considering
thermodynamics. We also clarify the interrelationships among the universal
relations.
