The fluctuation-dissipation theorem for non-Markov processes and their contractions: The role of the stationarity condition (Q1117613)

A demonstration is given of the equivalence between the stationarity condition of an N-dimensional stochastic process a(t), defined as the solution of a generalized Langevin equation with random initial values, with the (``second'') fluctuation-dissipation theorem. As a result, it is shown that a similar relation also holds for any stochastic process obtained as a projection of a(t) into a subspace of the original space.