The Matsubara space is a purely mathematical construction, but each dimension relates to both the physical characteristics and the magnitude of the Markovian constraint applied. In an overdamped hierarchy we require the sum of an infinite number of Matsubara frequencies where the first two frequencies (ν n0 and ν n1 ) are temperature independent and related to the bath dissipation rate, and subsequent thermal frequencies (ν nl ), which are complex, result from poles in the spectral function.