Linear Response and Correlation Functions

We consider a system in a stable steady state or in equilibrium. If we disturb the system by applying some external fields or by changing some parameter the system will be driven away from its former steady state. The external fields or the changes of the parameters are usually small. Then we only need to take into account those deviations from the steady state which are linear in the external fields (linear response). The deviations of expectation values from their steady-state values also depend linearly on the fields. This dependence can be described by a response function. If the external fields are switched off, the deviations from the steady state decay or dissipate (in the physical literature the word ‘dissipate’ is usually used for the decay of energy).